Conservative solutions to the black hole information problem

which provides a classification of solution attempts to the black hole information loss problem. As a warm-up, I recommend you read my post on the Black Hole Information Loss Paradox. You will notice that in this earlier post the basic argument of the paper is already outlined. The paper just makes the definitions more precise, and discusses the options one has to solve the problem based on how radical departures from semi-classical gravity they require. Not to mention that the paper has a lot of nice figures. We have made some effort to make the paper understandable for a broad audience, so don't be shy and download the full thing.

The Core of the Problem: The Singularity

The essence of the argument is the following: A singularity is something you don't want to cross your path. Why? Because infinities are dangerous. They crunch and destroy things, they literally set an end to existence, and in doing so they are indifferent as to what exactly crossed their way. A singularity is always singular. Infinity is always infinity. As such, crossing a singularity is an irreversible process. The problem is that once an initial state ended up being singular, you can't figure out what it looked like originally.

The problem with black hole information is that evolution is not unitary if you believe that the initial state of the black hole gets converted mostly into thermal radiation to excellent precision. Non-unitarity is generally considered an unappealing property because it is in conflict with quantum mechanics and can cause all kinds of nasty side-effects you don't want. But an evolution that is not reversible cannot be unitary. Reversibility is not a sufficient, but a necessary condition for unitarity. However, since irreversibility is a characteristic of the presence of singularities, first thing you want to allow for a unitary evolution is to remove the singularity. Classically, this singularity is unavoidable. But we know that close to the singularity the curvature gets very strong (into the Planckian regime) and classical General Relativity (GR) is no longer valid. It should be replaced by a more fundamental theory that can be expected to remove the singularity, though the details are not well understood today.

The paper offers a generalization of the classical singularities in GR that can be used for spacetimes that might have quantum gravitational regions. Throughout the paper we have tried not to make any specific assumptions about the unknown fundamental theory. The problem with the classical definition of geodesic completeness is that the notion of a geodesic, which relies on the presence of a metric, might not make sense any longer in the presence of strong quantum gravitational effects. The definition we are suggesting is motivated by the classical definition, and is then what I outlined above: a space-time is non-singular if evolution is time-reversible. It then follows trivially that a singular space-time generically suffers from information loss. Thus, a black hole space-time without information loss can not be singular in the so defined sense. If you want to understand what happens to the black hole information, first thing you should do is thus to get rid of the singularity.

It is honestly a mystery to me why some people are so obsessed with the black hole horizon, believing that the horizon is the problem. The horizon is not where information gets destroyed. It is merely some surface where the information becomes irretrievable from the outside. Not to mention that the horizon can be at arbitrarily small background curvature. One thus shouldn't expect any quantum gravitational effects to be relevant at the horizon, and no reason to seek a solution there.

Radical and Conservative Solutions

Removing the singularity removes an obstacle to unitary evolution, but it doesn't explain how information survives. In the paper we discuss the possibilities one has if one just accepts that quantum gravitational effects are negligible until the very endstate of the evaporation. These solutions we have dubbed “conservative” . Everything else that requires non-locality on horizon scales or quantum gravitational effects in the weak curvature regime and so on, we have called “radical”.

The conservative solutions can be classified into three cases. In all of them it is assumed the singularity is removed by quantum gravitational effects:

The information is released in the final Planck phase, in which case there never is a real event horizon (in the paper, that's option 3).

The information survives in a baby universe that disconnects from our universe ( option 4A).

The information survives in a permanent, massive remnant (option 4B).

Most importantly, conservative solutions imply that the endstate of black hole evaporation - when the black hole has about Planck mass and Planck size - carries a (potentially arbitrarily large) amount of information. The reason is simply that, if one accepts that the semi-classical approximation holds, Hawking radiation does not carry any information (except its temperature). Thus, the information has to remain inside. We thus have an endstate that must be able to store a large amount of information, even though it has a small surface area. This speaks in particular for the surface-interpretation of the black hole entropy. Objects with these properties are known to be possible in General Relativity, we have discussed such “bags of gold” and “monsters” in a recent post.

The three above mentioned possible cases have been discussed for some while in the literature until some time in the mid 90s. There are some objections to all of them that we address in the paper. All in all, though valid objections, they are not terribly convincing. It is thus puzzling to some extend why there hasn't been more effort invested in what seem to be the most straightforward outcomes of black hole evaporation. Unfortunately, I have had many times the impression these conservative solutions were abandoned prematurely for the sake of creating more fanciful radical solutions, for not say, absurd speculations.

A note on the definition of singularities we are using: If one had a fundamental theory to describe spacetime in the regions with strong quantum graviational effects, one could consider other notions of singular spacetimes, for example by using divergence of operators describing the background curvature or likewise. Then there arises the question how this definition would coincide with the one we have been using. One could imagine cases where they do not. Eg, the information of fields propagating in the background might not be sensitive to a curvature singularity, or the singularity itself could encode information.

Bottomline

The sane thing to do is to stick with conservative options until we are sure it's a no-go. That requires in particular understanding the properties of Planck-sized quantum graviational objects with high entropy.

210 comments:

Thanks so much for expanding the explanation of your paper. It does go a long way to increasing my understanding of what you’re proposing. I must say that I agree that the removing of the singularity seems to be a priority since no physical theory has advanced very far when faced with infinities that resist being discarded or rather a method found to work around them, such as renormalization represents as being in the advances of quantum theory such as quantum electrodynamics and all the other advances since.

“It is honestly a mystery to me why some people are so obsessed with the black hole horizon, believing that the horizon is the problem. The horizon is not where information gets destroyed. It is merely some surface where the information becomes irretrievable from the outside.”

The above was one of my favourite statements for I too have often wondered what all the fuss about the horizon was. It amounts to imagining that an efficient thermos bottle has serious consequences in relation to the second law, since we can’t observe or be certain of the temperature of its contents. As far as I’m concerned the event horizon represents to be no more then the most ideal bottle. With or without Hawking radiation it’s arbitrary to consider what’s inside the horizon to not being part of the system. Even in the classical view if one was to pass through it and look back the universe would be visible to remain, although the rate of its evolution relatively hastened. So how does this suggest a detachment as only reaching the singularity could accomplish that.

In the end like has been demonstrated in the standard model there are different stages in the resistance to gravitational collapse and I see this last one as being no different, just not understood to be explained. The one thing they share in common is that they are all dependant on the initial mass and the time required to evolve. My crude way of looking at it (and perhaps naïve)is the only way to end up with an infinity is to begin with one. In this case that would be to say that the only way to realize an infinite density is to begin with infinite mass.

Bee - It is honestly a mystery to me why some people are so obsessed with the black hole horizon, believing that the horizon is the problem.

Maybe it's because the existence of the horizon is what removes information from our universe. No horizon, no paradox.

You could blame it on the singularity, but what's the point if singularities probably don't exist?

The horizon is only non-special for an observer already committed to passing through it - the free falling observer. For an observer capable of getting close and then retreating, it's a hell whose temperature (due to the Hawking effect) is asymptotic to infinity. Isn't that true?

Sorry I forgot to add that my favourite scenario is that through Hawkings’ mechanism or something else that all the classical entropy (heat) be allowed to escape (return) leaving what remains to have between itself and what’s released as potential. That’s because it is potential that amounts to be the driving force of any system. So in this way perhaps black holes are the realization of Maxwell’s demon that permits a continuance of it all.

when I said that every fermion could be a bag of gold I thought, primarily, on the electron. When you renormalize a charge, you can say that a screening of virtual electrons that shields your detector from finding an infinite charge. But, if you are really close to an electron, well, you avoind the shielding and one finds a so strong EM field that you might find a mini black hole. So, instead of saying that you find a black hole, why not a bag of gold with a very strong EM field traped inside? You'd get the concepts of chage without relying on charge.

Make the bag of gold spin, you get spin.

I don't know if that is feasible. But it would be interesting to think about something similar to geometrodynamics, but without resourting to little wormholes, but as defects with almost-trapped surfaces that could actualy trap fields.

I though of this when I saw that one could find the residual of a black hole as a kind of bag of gold which is a kind of defect in space time which traps fields.

There are ways to produce charges without charge. Check the last pages of Frank Wiczek article,http://arxiv.org/abs/0812.5097

in which he also references this articlehttp://www.theory.caltech.edu/~preskill/ph219/topological.pdf

Yes, your paper with Smolin is a good one, for two reasons: first, the emphasis on *reversibility*, reminding us that the problem really is a thermodynamic one in some sense; and second, the gentle reminder that claims that the solution is to be sought near the event horizon are "not conservative" --- which is a polite way of saying "completely ridiculous".

However, here are two answers to your [or Lee Smolin's] question, namely: why hasn't the obvious solution [essentially, baby universes born inside black holes, as in cosmic natural selection] been followed up? The first reason is that nobody really knows *how* to follow it up! The second, and much better, reason, is that there are very good reasons to think that baby universes [of this kind, ie born inside black holes] won't be like ours --- they won't begin in a state of low entropy. So it's hard to see what use they are for explaining anything in *our* universe, apart from solving the information loss problem.

ps: as I said in your "monster" post, there are reasons to think that bags of gold don't exist in string theory. So that is an argument against remnants from a string point of view.

pps: You only mentioned Horowitz and Maldacena in passing, but I think that their idea deserves a lot more attention. It has been generally dismissed for very inadequate reasons.

All your conservative solutions macroscopically violate Einstein's equations, even in regions where the curvature is very low.

Whether or not the singularity is "infinite" or not is completely irrelevant for the information loss puzzles.

Even if it is regulated at short distances, which is how most people imagine it anyway (and the information questions really have nothing to do with the question whether this visualization is correct), the information gets destroyed there simply because there is no future-directed timelike trajectory from the vicinity of such a singularity to the exterior spacetime. The (semiclassical) destruction becomes inevitable at the moment of crossing horizon, for purely causal reasons, and trying to "solve" the information loss puzzle afterwords is simply too late.

Also, all the black hole information can't get away in the "last Planckian moment", or something like that. What does this option even mean for a large black hole? Should the black hole remember that it once used to be large, and recall all the information from those good old times when it was large, and emit all the information from those old times?

What if it had some life before it as well? Should it remember the state from the beginning of the Universe? It makes no sense.

Also, there are no numerous remnants because they would completely spoil the spectrum of the theory and would be produced generically. Baby Universe may look different for the infalling observers but they still look like remnants to the exterior world, so it is correct that you included them in the same category.

This category is excluded, too.

The macroscopic description of spacetime must clearly reproduce the diagram in your option (1), the only conservative solution, the only solution that macroscopically agrees with Einstein's equations, and the only solution that you don't call "conservative".

What you're writing is just completely weird. Note that capitalist pig is doing everything he can throughout his life to be against me and with my foes but he can hardly hide that he is beginning to understand these basic issues about the (ir)relevance of the horizon and singularity, too.

The corect solution is macroscopically (1) except that there are tiny "tunneling" effects that can imprint the detailed microstate into the Hawking radiation - fingerprints that are not visible semiclassically or in the whole perturbative expansion, for that matter.

why hasn't the obvious solution [essentially, baby universes born inside black holes, as in cosmic natural selection] been followed up? The first reason is that nobody really knows *how* to follow it up! The second, and much better, reason, is that there are very good reasons to think that baby universes [of this kind, ie born inside black holes] won't be like ours --- they won't begin in a state of low entropy. So it's hard to see what use they are for explaining anything in *our* universe, apart from solving the information loss problem.

Well, I am not a huge fan of the baby universe solution, but I think you are confusing two different things here. The baby universes in the sense we have discussed them in the paper are indeed not like our universe. To begin with, they are closed. And yes, they generically have a large entropy. But they are not supposed to be like our universe - I think you might have CNS in mind, but we haven't tried to make an argument about that. Yes, the use they have is they provide one solution to the information loss problem.

I like the Horowitz and Maldacena idea, but their motivation could be stronger. I am sure we will hear more about that.

Well, you don't need an infinite mass to create an infinite density. You just have to squeeze it together to one point. Now one would expect from quantum gravitational effects that this can't happen, thus no infinite densities, thus no singularities. I think almost everybody expects that quantum gravity will take care of the singularities in classical general relativity. I just think that the relevance of that for resolving the information loss problem has not been reflected well in the literature. Many attempts focus on the problem of how to shove the information through the horizon. Which, when done before the final stage, necessitates locality violations.

The difference to the bottle you are comparing the black hole to is that the region inside the horizon is indeed causally disconnected from the outside. Also, radiation can very well fall into a black hole, it just can't come out. I think the analogy to a one-way membrane is quite helpful in this regard. Best,

Bee: I'm not going to get into the conservative versus not conservative issue, those are just words. In AdS/CFT we have a detailed understanding, backed up by a large body of calculations, demonstrating how apparent information loss comes about, how it is related to the horizon of the black hole (roughly, the infinite red shift makes the spectrum continuous), and how it is solved in the dual field theory which encodes all the fine details of the problems, neglected in GR.

So, the situation has changed, and in my mind any other of the classic, well-known solutions to the problems has to be equally quantitative to earn my respect. Are there any new arguments for the "conservative" solutions, or at least new arguments against their well-known problems?

But to one of your issues, how can anything happen at the horizon even if the curvatures are arbitrarily low. This is also well understood. In any quantum mechanical system with large degeneracies (as is typical for highly excited states), the following holds. If you calculate simple quantities, you in effect average over huge number of states, obtaining a thermodynamic averaged quantity. For those you can use perturbation theory, the effect of any perturbation on the level will be small. For detailed quantities like the correlations between macroscopic number of Hawking quanta, perturbation theory breaks down for arbitrarily small coupling. Same happen in this situation: for average thermodynamical quantities you can use GR, and to understand subtle issues to do with unitarity, quantum gravity is needed.

Maybe it's because the existence of the horizon is what removes information from our universe. No horizon, no paradox.

I am certainly not telling you what you are allowed to find paradoxical. But the horizon does not 'remove information from our universe' - it just avoids information can reach I^+, and as far as I am concerned not being able to access information in some region of spacetime is not particularly paradoxical. The problem is that if the black hole evaporates into purely thermal radiation, this region shrinks away and information does never come out (if radiation remained purely thermal that is). What is paradoxical is that blaming the loss of information on our lacking understanding of quantum gravity does not seem to be sufficient to solve the problem (for reasons that I am sure you are well aware of, explained in the above mentioned earlier post ).

You could blame it on the singularity, but what's the point if singularities probably don't exist?

The point we were making is that understanding the avoidance of singularities is necessary to solve the problem since it is actually the (classical) singularity where information gets finally destroyed. That does not mean it is sufficient though. The argument is simply as long as you have a singularity (in the sense defined) you have a problem.

The horizon is only non-special for an observer already committed to passing through it - the free falling observer. For an observer capable of getting close and then retreating, it's a hell whose temperature (due to the Hawking effect) is asymptotic to infinity. Isn't that true?

And if you'd have an observer with infinite acceleration in flat space he'd also see a hell of particles. So what's your point?

Thanks for the link. I still don't see what this is good for. Does it help me to understand anything? Like, why are the masses of charged particles not continuous and have the values they have? Also, how do you get a solution with non-vanishing trace of the energy momentum tensor from stuffing EM fields into the bag? Best,

I am sure you could answer all your questions if you would actually read the paper. I am not interested in fighting with you about terminology, but what you refer to as 'destruction' of information, is merely the event of it becoming unavailable to the observer at I^+. And yes, you are of course right, once you have crossed the event horizon you are stuck inside it, that's more or less the definition of horizon (which is also in the paper).

Should the black hole remember that it once used to be large, and recall all the information from those good old times when it was large, and emit all the information from those old times?

I am not sure what you mean with 'remember', but it simply stores everything that falls in, yes, from those old times.

What if it had some life before it as well? Should it remember the state from the beginning of the Universe? It makes no sense.

Things that don't make it inside the trapping horizon of course don't have to be stored.

In our terminology the difference between baby universes and remnants is in their ADM mass. It's zero for the former, non-zero for the latter. But yes, they are related in that both are permanent and just keep the information.

Ya okay, people have problems and use the horizon. Does it change the way the problem existed for them if they try and describe it another way? The Thing?:)

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.Black Holes and Beyond: Harvard's Andrew Strominger on String Theory

Susskind presents the "Gedanken experiment" to summarize and bring us up to date. Of course, there is a lot history behind this.

Does this understanding help too, "not cross paths with the singularity?" Maybe some might like the Klein bottle(rain drop) for a comparison then if it were ever the case that such an evolution to the singularity was just the "turning" inside out? :)

Stefan… actually it was a coincidence, and from what you point out, a nice one. I don’t know anything about the mathematics of droplets, but it seems likely that there’d be a singularity, indeed. No, Dave did not talk about this, as far as I could tell.

if the black hole were storing the information about all the matter that every fell into it, but were not losing this information as it evaporates, it would mean that such a black hole must be capable to store an arbitrarily high amount of information - it would have to accumulate everything that went into it, without losing it. Just think of a black hole that was absorbing and emitting matter for 5 billions years at the same rate.

That would mean that pretty much arbitrarily small regions of space can carry arbitrarily high information. That's impossible - e.g. because the loop processes involving these new objects would always diverge. There are much less dramatic possibilities that can be easily excluded. For example, virtual effects of any remnants will drive Newton's constant to zero.

Of course, in Matrix theory or the AdS/CFT, one can see that there are no remnants, no baby universes, and no unlimited storage of information in a black hole. But even if one chooses to ignore these "models" of quantum gravity as a qualitative template, the room to maneuvers is just incredibly constrained these days.

Wow, I was at least assuming that your baby universes behaved as massive remnants for the exterior observers in the old Universe, too. Now you want the baby universes (that can carry all the information) to look like *massless* particles in the old Universe? That's really... bold. ;-) Infinitely many new massless particle species, right?

Massless particles have a tremendous effects on physics. For example, massless bosons always cause long-range forces. You seem to be adding even more "conservative" (in your terminology - note how polite I am) items to your picture than what you have written in the article which is more incredible than before.

I don't know. We actually haven't talked about that. I would be in favor of submitting it somewhere. However, as I also wrote in the post, the paper is a classification of solution attempts, not actually a new result. It's not the kind of paper I usually write, so not sure how difficult it would be to publish. It also serves its purpose well on the arxiv. Best,

But to one of your issues, how can anything happen at the horizon even if the curvatures are arbitrarily low. This is also well understood. In any quantum mechanical system with large degeneracies (as is typical for highly excited states), the following holds.

Why do I have highly excited states if the curvature is arbitrarily low? Best,

I think it would really help if you would read the paper. Or at least my post. This would answer a lot of your questions, and save me a lot of time.

if the black hole were storing the information about all the matter that every fell into it, but were not losing this information as it evaporates, it would mean that such a black hole must be capable to store an arbitrarily high amount of information - it would have to accumulate everything that went into it, without losing it. Just think of a black hole that was absorbing and emitting matter for 5 billions years at the same rate.

Correct.

That would mean that pretty much arbitrarily small regions of space can carry arbitrarily high information.

They can have an arbitrarily large volume.

That's impossible - e.g. because the loop processes involving these new objects would always diverge.

If objects with an arbitrarily large volume would appear in loop-processes, which doesn't seem particularly plausible to me. But either way, the question of whether or not there can be an effective theory for such objects is discussed in the paper.

Wow, I was at least assuming that your baby universes behaved as massive remnants for the exterior observers in the old Universe, too. Now you want the baby universes (that can carry all the information) to look like *massless* particles in the old Universe? That's really... bold. ;-) Infinitely many new massless particle species, right?

Massless particles have a tremendous effects on physics. For example, massless bosons always cause long-range forces. You seem to be adding even more "conservative" (in your terminology - note how polite I am) items to your picture than what you have written in the article which is more incredible than before.

No, these objects actually look like 'nothing' in the old universe. They have neither mass nor momentum, they are simply disconnected.

From the viewpoint of an outside observer, a black hole is a state of an energy equaling its ADM mass. For large black holes this energy is large compared to the energy scale of fundamental excitation (the Planck mass). This is the origin of black hole thermodynamics, a generic highly excited state in a generic theory will have a thermodynamic description, as far as simple quantities are concerned. It is only when probing fine details that you need the microscopic description.

To probe the microscopic details of any complicated system, black hole or gas in a room, you'd need to calculate very detailed quantity. For those detailed quantities perturbation theory tends to break down, at arbitrarily low couplings. This is a generic phenomena, so we should not be surprised that it is also true in the black hole context.

BTW, what I was asking is whether the status of those conservative solutions has changed some in the last X years, where X could be your choice. I really don't know, those tend to be the solution favored by the relativity community. References would be appreciated.

Not to put words in Moshe's mouth, but I think the trouble is that you don't seem to address the now standard and well-supported picture of the resolution of the information paradox. Namely, that Hawking radiation is not precisely thermal; there are correlations in the Hawking radiation which allow the information to escape, but they are small (e^-S, with S the black hole entropy), and don't show up in the semiclassical analysis. Everyone would agree that the singularity is a classical artifact, and that there is a well-defined nonsingular quantum evolution. The question is why is the semiclassical calculation misleading, and this is a question that can be asked entirely in the weak-curvature regime. The answer is that these small effects are not accounted for. The "highly excited state" we're concerned with here is the black hole itself, which has very high entropy; the classical analysis is coarse-graining all these states into one black hole, which is roughly speaking why it's giving you a thermal answer that overlooks the correlations.

Why do I have highly excited states if the curvature is arbitrarily low?

Well, black holes of a large mass are excited states because the more energy (=excitation) one adds to it, the more massive they become (by the mass conservation and by E=mc^2).

More excited i.e. more massive black holes have a low curvature outside the horizon because this fact can be calculated from general relativity: the radius (of curvature or event horizon) scales like the mass in 4D (or a positive power in other dimensions).

Time to return to Moshe's words. A very excited (massive) black holes has a large entropy i.e. many microstates. Averaging over them is a kind of thermodynamic limit that will represent the interior as being empty, even though the content of the BH interior depends on the microstate if one avoids the averaging.

I've read your paper. Maybe the reason of my (and others') "opinions" about the black holes is different than not having read your paper? Just a speculative idea to consider! ;-)

If the baby universes look like nothing and get disconnected, then they don't exist for the observers in the old Universe and the information, as compared in the information loss puzzles (which is always comparing information in the same Universe, before the BH creation, and after its evaporation) is lost or not lost in the same way as if the baby universes were not there at all.

They are not there, after all, in this case. Such disconnected universes have no impact on the information loss or preservation.

Yes, it is probably not so surprising that these solutions tend to be favoured by the GR community. As far as I know there hasn't been much work on that since the mid 90s, except for Steve Hsu's recent papers (see earlier post).

I think you are making some assumptions as to what the microstates of the black hole do describe. Besides this I don't understand how what you say explains how, microscopically, the information from an infalling piece of matter (quantum state, whatever) gets transferred into the outgoing radiation?

I really like the "baby universe" idea. The remnant in the parent universe could be a Planck mass black hole aka graviton 4-pair that effectively creates a deadend in spacetime (a discrete spacetime). The information of a Planck mass black hole could very well be the information for an instanton big bang like ours (a Paola Zizzi idea).

Yeah, what you consider conservative depends strongly on your background. If you think the geometrical description of classical GR is complete, you'd tend to favor solutions where this structure describes the situations very far from where it was ever tested, e.g in the interior of black holes, even if this leads to results which look very strange from ordinary quantum mechanics viewpoint.

I don't know in precise detail how the information is transferred to the Hawking radiation. Then again, I don't know that for ordinary process like burning a piece of coal, and I trust that QM is fine with those processes on much less detailed evidence. That much less detailed evidence pretty much exists already for black holes in AdS space, though it is still interesting to phrase it in the gravitational language.

these questions about progress in other directions can be pretty quickly answered e.g. by Google Scholar. Take e.g. black hole remnants.

You will see a 2001 paper (Adler) arguing that something must be left by a new uncertainty principle, but they don't say much about the spectrum of the left things (so it could be just one particle).

Otherwise, there are a dozen of high-cited papers of the type "If there were remnants, we could see them, they could be.... dark matter or whatever", but none of these papers seems to contain any model or theoretical evidence that the remnant picture makes sense.

You will find Bekenstein, Banks, Strominger etc. among the top-cited authors with the keyword, and you may know what they think today.

Similarly, you can browse through the baby universe papers. You will probably know quite a few. The others will be very similar to the Sabine Lee paper, as far as the content goes.

The most famous star-like, no-horizon, no-singularity paper to modify the picture is probably by Ashtekar and Bojowald. You may look at it whether it will convince you that it contains some new evidence for anything. I have personally no idea why they think that they allowed the things from the BH interior to escape, completely changing the diagram. I haven't read every word of the paper but it just looks wrong.

These were the three "conservative" solutions and I am afraid that you won't find any better papers to support these "conservative" choices. So I guess that you will silently agree that the "preference" of these "conservative" solutions by a whole "relativistic community" is due to nothing else than zeal.

I think the trouble is that you don't seem to address the now standard and well-supported picture of the resolution of the information paradox.

Well, the thing about the information loss is that people like to argue about it and everybody has his or her favourite solution. You evidently don't like we haven't spend enough time in discussion the one you like best. Sorry about that. Besides this, same question to you as to Moshe: how does in that case, microscopically, the information get from the infalling to the outgoing particle at the horizon?

One more comment for Moshe: note that if the "conservative" terminology depends on the background, the communities have been reverted.

Clearly, the normal macroscopic Penrose diagram of a black hole is "conservative" for us because it actually follows from general relativity. It is very strange for a relativist to deny it and consider this denial of relativity "conservative" according to his upbringing.

It would be more logical for him to argue that the diagram is correct and the information is simply lost, just like Hawking did, by causality.

I think you are making some assumptions as to what the microstates of the black hole do describe.

I thought that microstates of a black hole describe microscopic states of an object called a black hole. They're vectors in the Hilbert space and their precise dynamics is described by the dynamical laws of a theory - e.g. a Hamiltonian. We can also ask whether we should love them or imagine them but these aspects are not a part of real science, are they?

Besides this I don't understand how what you say explains how, microscopically, the information from an infalling piece of matter (quantum state, whatever) gets transferred into the outgoing radiation?

Any glowing object imprints the detailed information about the microstate into the radiation, and black hole is no different. The only reason that was thought to make it impossible was causality - the causal separation of the interior where the information was imagined to reside. But this causality turned out to be just an approximate feature arising from the averaging over all microstates.

Individual microstates don't respect the causality, the "empty interior" picture of the black hole is not appropriate for them, and they get the information out in the very same way as a burning preprint.

Well, the thing about the information loss is that people like to argue about it and everybody has his or her favourite solution.

Has physics been reduced to sentiments and popularity polls, making the actual papers and evidence obsolete? That's very bad but fortunately in this particular case, the stringy picture wins, anyway. ;-)

More excited i.e. more massive black holes have a low curvature outside the horizon because this fact can be calculated from general relativity: the radius (of curvature or event horizon) scales like the mass in 4D (or a positive power in other dimensions).

Doesn't the curvature at the black hole horizon scale as M/R_h^3 ~ 1/M^2? Anyway, I certainly never questioned the curvature is low at the horizon.

Time to return to Moshe's words. A very excited (massive) black holes has a large entropy i.e. many microstates. Averaging over them is a kind of thermodynamic limit that will represent the interior as being empty, even though the content of the BH interior depends on the microstate if one avoids the averaging.

According to what theory?

I've read your paper. Maybe the reason of my (and others') "opinions" about the black holes is different than not having read your paper? Just a speculative idea to consider! ;-)

In this case it is very depressing you weren't able to extract from the paper that baby universes disconnect from the externally flat region, since this is basically their definition. Moreover, the fact that their volume can be arbitrarily large seems to have somehow escaped you, even though we have spend several pages discussing that point.

If the baby universes look like nothing and get disconnected, then they don't exist for the observers in the old Universe and the information, as compared in the information loss puzzles (which is always comparing information in the same Universe, before the BH creation, and after its evaporation) is lost or not lost in the same way as if the baby universes were not there at all.

They are not there, after all, in this case. Such disconnected universes have no impact on the information loss or preservation.

The point is that the evolution is unitary if you take into account the baby universes. It just looks non-unitary to the observer in the asymptotically flat region, because he has no access to part of the space-time, which results in his quantum state being mixed. The important thing about the baby universes is not that they "are not there" in the final state ("there" presumably meaning connected to the asymptotic region) but that they were there in the initial stage, and information ends up in them.

“Well, you don't need an infinite mass to create an infinite density. You just have to squeeze it together to one point”

Yes I understood this before I said it, as I know that a point represents in theory as a place with proximity (location)yet of no physical size, which when considered as part of the whole equates to be what one gets when you divide something by zero. As I understand it in the mathematical perspective this has it to be undefined, rather the infinite. I certainly won’t belabor the point (no pun intended), yet I do see as significant to differentiate undefined from infinite, for the former I see as paradoxical and therein perhaps wrong, while the latter I see as a limit which defines the absolute boundaries that can be considered. So as opposed to a point, if as you and others have contended we are limited to a definable size, then to achieve infinite density would require infinite mass. I’m sure this along with other considerations is what lays at the heart as to why many are convinced that a singularity cannot exist.

“Also, radiation can very well fall into a black hole, it just can't come out. I think the analogy to a one-way membrane is quite helpful in this regard”

Yes as I said the analogy is crude, yet as you remind that by thinking about it as a Maxwell’s Demon does lend it this one way aspect. To be truthful I’m still hung up when information and (classical) entropy are taken as being one in the same, as the forner more relates to me as specific (meaningful) ordering and the latter the process that serves to eliminate any such distinction as the limit is random, which in effect leaves no backwards trail to follow other then to be able to say what was before was more ordered. This I find to be not merely trivial, yet deceptive as to opposed to what normally is imagined as what information truly constitutes as being.

Anyway all this is truly interesting and as I can tell from the shear volume of post activity highly contested. Which ever way it turns out to be Black Holes and their implications certainly serve as a linch pin for future discovery. It is of little wonder why above all else one of the things that bothered Einstein the greatest is that his theory inevitably leads to such implications. In that regard I’m currently reading John Moffat’s new book “Reinventing gravity”. Perhaps this can offer additional thoughts on how the problem might be approached? Not that I would even consider such a challenge as I’m far from capable yet merely insatiably curious.

By the way with all the comments I’m having difficulty being able to distinguish between “Peer Review” And “Peer Revile” :-)

Sorry for the misunderstanding. You are right of course, if you can't squeeze matter into a point you need an infinite mass to get an infinite density. However, mathematically speaking infinities are nothing particularly worrisome. Infinity is a very well defined concept, one can deal with it very well. The worries with singularities are physical, not mathematical. What does it mean for something to be "really" infinite? Do such events exist? I don't know, honestly, but I think the general sense is that a singularity indicates the breakdown of the theory and signals that it has to be replaced by a more fundamental theory that can be trusted better.

I didn't ready John's book. Let me know what you think if you are done!

Dear Sabine, happily enough, we agree that in 4D, the radius scales like the mass so the curvature scales like 1/M^2. Do you still agree that for large (heavy) black holes, the curvature is small?

I don't know exactly what positive thing you had in mind but you had an apparent difficulty with Moshe's description of black holes as highly excited states with low curvature.

According to what theory?

According to any theory of quantum gravity - but if you don't find any papers with that statement, you may interpret the statement as my discovery, work in progress. ;-)

It is very easy to see that many microstates of a black hole don't have an empty interior. For example, when a spaceship just fell into the black hole, there is a spaceship inside the black hole, so it is not true that all black hole microstates are empty inside.

On the other hand, having a spaceship in a black hole is a nontrivial condition that chooses non-generic black hole microstates. The generic states can't have any spaceships and they look contrived. For example, the "fuzzballs" (including LMN bubbles in AdS) give very nontrivial profiles for black hole microstates.

All these subtleties go away with the averaging which must clearly generate translation invariant physics, even locally, because the whole "ensemble" of microstates is clearly invariant under these things, and the empty BH interior is the only dynamics one can get in this way.

Again, yes, it is plausible that not many people realize that things work in this way, even in the "stringy culture", but they will surely agree when they sort it in their heads.

Baby universes

Again, if the Hawking radiation carries no information about the initial state, and the information is stored in some other Universe, then the definitions of the information loss problem say that the information has been lost.

More precisely, it has been lost for the physical observer.

That's also why the information loss problem wasn't a problem before Hawking discovered the radiation: one could always say that the information was inside. The problem only became physical once the black hole could disappear because one could no longer argue that the information is in it.

If you want to count the information in some completely different, physically inaccessible universe as "stored" or "preserved", you may also equally safely save your money in banks in another Universe that has disconnected from ours. Happy saving, Iceland may be better, after all.

Let me explain the "empty black hole from averaging" differently. If one waits for a while, complicated excited bound states get "thermalized" - one gets generic microstates or their mixture out of pretty much any initial state.

With the spaceship in mind, we have another way to describe what the "waiting" means for the black hole. The black hole simply sucks everything that is already inside, flying towards the singularity. After some time, in some appropriate coordinates, all these things are swallowed by the singularity and the interior is emptied.

Also, the quasinormal modes (vibrations of the shape etc.) exponentially drop almost to zero. The black hole becomes spherical and empty. Microscopically, we saw that it must be the same thing as getting a typical microstate - or the average over pretty much all of them. That's roughly why the average over microstates must be equivalent to the empty interior. (Black holes are the fastest thermalizers in the world.)

The opposite statement, that non-averaged microstates are not empty inside, can be seen with the spaceship - or with the fuzzballs, if you wish. A lot of the confusion about the information loss was caused by incorrect identification here.

People often thought that all microstates still looked empty, or that the "spaceship inside" carried additional degrees of freedom besides the black hole microstates. Of course, it can't. The black hole microstates count all possibility that can exist inside the [stretched] horizon, so they already contain all configurations of spaceships, too.

Averaging means "empty interior", microstates are not empty and don't allow us to separate the interior from the outside world in the same way we do for empty black holes. (Generic BH microstates are much further from the empty BH than a BH with a spaceship.)

You saythere are correlations in the Hawking radiation which allow the information to escape, but they are small (e^-S, with S the black hole entropy)

I understand that this is the conventional string theory wisdom. But if the correlations are exponentially small, how can they possibly carry more than an exponentially small amount of information? Is this explained anywhere? It is an easy calculation that they need to carry a lot more information than e^-S if the information is to escape.

This may depend on your definition of exponentially small, which is an incredibly vague term.

Your commentIndividual microstates don't respect the causality, the "empty interior" picture of the black hole is not appropriate for them, and they get the information out in the very same way as a burning preprint.

reminds me very much of the famous Sydney Harris cartoon. I think you be more explicit here in step two.

Peter Shor: let us forget about black hole and try to find out what is the precise microstate of the air in your office. There are many ways to find out, all highly theoretical. They may involve making very detailed measurements, or finding very fine details (which are "exponentially small") of a few simple ones. Eventually you'd have to gain access to S bits of information, where S is the entropy of the system. This applies equally to the air in your office, or to the Hawking radiation emitted from BH.

Lubos: thanks for the references, you'd see my opinion by what I choose to work on...while we are on the subject, I am wondering what is your preferred resolution of the paradox, as phrased in the gravitational language.

the term "exponentially small correlations" may be vague in the blog thread above and you may want to keep it vague - but you don't have to, if you follow me! ;-)

If you open Maldacena's 2001 paper, a favorite one of Moshe, it explains, see e.g. 5th line on page 14/20, that some correlations decrease exponentially fast. One can add an operator on a different - very separated and seemingly unimportant - boundary for similar exponential reasons but it is enough to restore unitarity, in a completely explicit way.

This AdS eternal toy model has a different geometry than the Schwarzschild black hole in 4D but the problems and their solutions are morally isomorphic.

You know, more generally (not related to Maldacena's paper directly), correlations may be exponentially small, but there are many types of correlators one can construct, and by combining them, they can carry sufficient information.

Moshe: I thought everything I wrote above was about my preferred solution in the gravitational language. I just believe that the microstates are really similar to the fuzzball picture, i.e. very far from a black hole with an empty interior, and then it is like any other burning object. One can still imagine that the black hole is "mostly empty" inside, but this always assumes some averaging over microstates already. I agree with you.

There can still be another picture that is consistent with all we say, like one based on black hole final state - but I doubt this particular one. The fuzzball-like constructions also suggest that non-BPS black holes probably have stringy modes in the "interior" excited, not being just SUGRA solutions, so I don't really believe that a "purely gravitational" description can carry all the necessary information (or degrees of freedom). What do you say, if you simplify your testimony relatively to things written above? ;-)

Moshe and Lubos have already given answers, but just to be clear, you're right that for certain quantities a semiclassical, effective field theory sort of calculation will just be wrong by an order-one amount. But those are quantities that involve correlations among a large number of quanta of Hawking radiation. If you stick with a very simple quantity, like some two-point function, the corrections will be exponentially small.

One can have some fun looking at N by N matrices and building simple toy quantum mechanics examples that illustrate such points....

One more clarification to Peter Shor: if you want to have a microscopic description of the air in your room, the easiest is to work in terms of the microscopic constituents. We have such an understanding of (Maldacena's version of )the information paradox for large black holes in AdS.

However, the gravitational language is analogous to the thermodynamical description of the system. Describing the specific microscopic situation if you have access only to thermodynamic measurements is tough, because you tend to average over huge number of states. The information about the specific microscopic situation is encoded in exponentially small contributions to such average quantities. It is precisely because they are exponentially small that they carry a lot of information - there are a lots more possibilities to consider if you are more sensitive to fine detail.

Just for the case that onymous is e.g. Joe Polchinski who would never dare to promote his own work, here is a relevant paper about the matrices as a toy model for black holes, Polchinski et al 2008. They show that at all orders in 1/N, probably analogous to orders in G_Newton, the information seems lost but it is preserved for finite N.

Matrix quantum mechanics is popular as a toy model for BHs - and maybe more than toy model - elsewhere, too. Susskind et al. 2008 argue that BH, much like matrix models, are the fastest thermalizers. This link is no coincidence because matrix models is how states - and black holes are generic localized ones at an energy level - are described in Matrix theory.

This paper by Susskind et al. suggests that the bits can "spread" over the horizon much like if all the possible links or synapses or what's the word between all the bits on the horizons existed - so the information on the horizon is stored like on an infinite-dimensional space, reducing a power-law growth of the thermalization time to a logarithm.

The misunderstanding is principally of my doing as I sometimes imagine that others will naturally fill in the blanks. As for Moffat’s book I have not much to report as I’ve only just begun. What I find somewhat frustrating, primarily as it’s time consuming, is that despite being nothing more then a novice I’m forced to read through many chapters of things that I’ve been long since familiar; yet have no choice for fear I might miss some important detail if I skip further along to the meat of the matter.

I can therefore only imagine how this must be for you and others who have this as their profession when picking up to read such a book. Perhaps like children’s toys there should be a couple versions written that would take this into consideration and so identified. At least for the pro this constitutes simply reading the authors latest and or most relevant papers. Then again, I really shouldn’t complain as Moffat is lending an opportunity for those like myself would not have if he considered such projects as being a waste of effort and in that sense not worthwhile.

Okay, then to begin with the introduction, “In 1916 Einstein published his new theory of gravity called general relativity. In 1919 the theory was validated by the observation of the bending of light during a solar eclispse,………..”

Hi Bee,"Like, why are the masses of charged particles not continuous and have the values they have?"It would be constant because it would be bounded by the "mouth" of bag. If the renmaints of the black holes are stable, they should be pretty much "static" objects.

I have no idea of why these would be any leftover from the blackhole. After all, the tiniest black hole should be a really heavy particle and decay into a shower of particles as fast a planck time. But, by admiting it it is a stable particle, I suppose it would be pretty natural if any particle is also candidate for a residual black hole, and so, a bag of gold.

This is, I think, another reasoning that would lead me to think that fermions have such nature.

"Also, how do you get a solution with non-vanishing trace of the energy momentum tensor from stuffing EM fields into the bag?"

I do not know whether anybody here said it already, but there is an easy way to see that the singularity is not the one to blame.

There are examples of three dimensional black holes (in AdS3 space) which have no curvature singularity whatsoever (these object have an event horizon) and yet the paradox exists. Therefore, the story is not related to what Bee is trying to say, and all the attempts to associate the physics with the singularity can not hold water.

It may be nice or sexy, but mathematically and physically we know it is wrong due to the existence (more than a decade) of counterexamples (the BTZ black holes).

A line of argument that is complementary to that taken by you and Lee in your paper is that if a theory of quantum gravity eliminates the occurrence of actual physical singularities that can destroy information, then that theory also rules out 'radical' solutions to the information paradox such as black hole complementarity. Black hole complementarity, as proposed by Susskind and others for instance, depends on the existence of a real singularity at r = 0 that destroys the information carried by an object passing through the horizon. If that information is not so destroyed, the 'complementary' copy of the information encoded on the stretched horizon can be collected and passed through the horizon to be compared with the original version at some later time -- in violation of the strictures against quantum cloning.

The existence of an actual singularity is thus crucial for the viability of black hole complementarity. However, the general expectation is that a realistic theory of quantum gravity will not contain such actual singularities. Your 'conservative' solutions to the information paradox would seem to be not just a less 'radical' option, but actually the only option if there are no actual spacetime singularities in quantum gravity.

1. AdS is totally, utterly different from the real world. I find it very easy to believe that the AdS/CFT explanation of the information problem is *correct* for AdS black holes.....and yet *utterly irrelevant* to the solution of the problem in the real world [and that goes double for the amazingly hyped BTZ black holes --- in 3 spacetime dimensions! "Leaving aside the fact that the asymptotics are radically wrong, and so is the dimension, the BTZ black hole is *exactly like* a real black hole...." Please.]. All we have seen contra this is statements using the word "morally". For all we know, as based on actual calculations, the correct statement could be: "Unitarity is preserved for black holes in AdS, but not in dS". I'm not saying I believe this, just that *nothing* that has been said here provides any evidence against this statement. Note that the distinction between large and small AdS black holes is irrelevant -- please bear in mind that black holes are intrinsically global objects. This observation leads me to.....

[2] In 2005, George Chapline gave a talk about black holes at Harvard. Here is what Jacques Distler had to say about that:

http://golem.ph.utexas.edu/~distler/blog/archives/000530.html

I urge everyone to read that, and to consider replacing the name "George Chapline" by "Samir Mathur". OK, I admit that the comparison is not completely fair. But nor is it completely *unfair*....

[c] The Horowitz-Maldacena proposal recognises the obvious fact that the singularity [or whatever replaces it] is the only sensible place to put whatever weird stuff is going on, yet it preserves unitarity in the "ordinary", stringy way. It is "radical" in Bee+Lee's sense, but to my mind it is the most conservative solution of all.

Thanks you for expanding the explanations of your work. Could you please elaborate on the folowing points:

1) what motivates the attitude towards maintaining unitarity through removing the singularity? While quantum physics is deeply linked to the concept of unitary evolution, non-equilibrium dynamics and non-equilibrium field theories are manifestly built on a non-unitary foundation. Why should one insist that equilibrium physics remains valid in strongly coupled gravitational regimes?

2) according to one of your earlier replies to my questions, astrophysical observations alone cannot settle the issue of where the BH entropy is coming from. Then how can one resolve the information paradox without having verifiable claims on the nature of BH entropy?

3) You conclude:

"The sane thing to do is to stick with conservative options until we are sure it's a no-go. That requires in particular understanding the properties of Planck-sized quantum gravitational objects with high entropy."

How can one ever hope to understand the physics of such "quantum gravitational objects" at the unreachable Planck scale? Isn'it wishful thinking?

I am perfectly sure I never doubted, neither here nor anywhere else, that the curvature at the black hole horizon is small compared to the Planck scale for large black holes (ie with masses larger than the Planck mass). I have no clue what you are trying to say.

Individual microstates don't respect the causality, the "empty interior" picture of the black hole is not appropriate for them [...] It is very easy to see that many microstates of a black hole don't have an empty interior.

I don't know who or what you are arguing with, but I never said anything of the sort that the black hole interior is empty or whatever it is you are trying to say. I also don't know what it means for a microstate not to respect causality, what exactly do you mean with that?

On the other hand, having a spaceship in a black hole is a nontrivial condition that chooses non-generic black hole microstates. The generic states can't have any spaceships and they look contrived. For example, the "fuzzballs" (including LMN bubbles in AdS) give very nontrivial profiles for black hole microstates.

All these subtleties go away with the averaging which must clearly generate translation invariant physics, even locally, because the whole "ensemble" of microstates is clearly invariant under these things, and the empty BH interior is the only dynamics one can get in this way.

Ah. And exactly how is this compatible with your above, correct, observation that what has crossed the horizon stays inside, and moreover can't even stay close by the horizon? I'm asking for a local dynamical explanation for what happens to the information. As far as I know fuzzballs create significant distortions of locality at horizon scales.

Again, if the Hawking radiation carries no information about the initial state, and the information is stored in some other Universe, then the definitions of the information loss problem say that the information has been lost.

More precisely, it has been lost for the physical observer.

Correct, it has been lost for the physical observer in the asymptotically flat region. The point is however that the evolution remains unitary if you take into acount the full endstate, which includes the disconnected part. I personally don't think that's such a particularly compelling scenario, but it's certainly a possibility.

That's also why the information loss problem wasn't a problem before Hawking discovered the radiation: one could always say that the information was inside. The problem only became physical once the black hole could disappear because one could no longer argue that the information is in it.

There are examples of three dimensional black holes (in AdS3 space) which have no curvature singularity whatsoever (these object have an event horizon) and yet the paradox exists. Therefore, the story is not related to what Bee is trying to say, and all the attempts to associate the physics with the singularity can not hold water.

Your argument is a non-starter. A) I was explicitly not referring to curvature singularities, but more importantly B) I wasn't saying if you don't have a singularity, you don't have a problem. I said as long as you have a singularity, you certainly have a problem. If you want to provide a counterexample, you'd have to find a case with singularity but without paradox, and not a case without singularity but with paradox.

Just another off the wall thought (or more likely a stupid question)and that is if as in quantum physics all that should be considered as being information is the wave function, then everything that follows is simply what manifests as a result: in other words what evolves. So the space required to hold a single wave function would not be very great, although necessarily less then zero (a point).

The question then is to ask, if this evolution is then deterministic or not? Standard quantum theory insists that it’s not, thus what is referred to as information is then arbitrary (and therefore trivial), while if it is considered as deterministic it then is significant (yet not fundamental in itself). It is then of course further required to discover if the wave function is fundamental in its beginnings and description or itself arbitrary. I find it strange then that when physics searches for a TOE in attempting to simplify, while insisting that nature itself is denied the same, as it’s required to preserve every insignificant aspect. Is this then to be considered reductionism or redundantism ? ;-)

Pope: nobody is claiming the dS and AdS are in any way similar. The large black holes in AdS are actually very different from that in flat space, in that they are eternal.

The point is that in that context one can make precisely the same arguments that Hawking makes for information loss, and see that they fail, and precisely how. Yes, it is a logical possibility that those arguments somehow fail in AdS (with arbitrarily low cosmological constant) but are still valid in flat space or dS space. It is a matter of personal taste if you regard such attitude as keeping your head in the sand, or being conservative and cautious.

One feature of the information paradox in the eternal context is that the singularity is always spacelike separated from an external observer. So, without macroscopic violations of causality you can do whatever you like at the singularity, it will have precisely zero effect on the information paradox. In flat space there is a small possibility the singularity becomes relevant at late times, this possibility is eliminated in the eternal case.

They study the CGHS model and show in detail that the singularities in black holes are eliminated by quantum effects and the evolution completely unitary. This is a PRL, more details are coming in a long paper, some of which were discussed in a recent talk: http://pirsa.org/08120016/.

There has also been a lot of progress showing that the singularity is eliminated in homogeneous models of black hole interiors. See, for example, papers by Leonardo Modesto:

There are other papers in this domain, for example, Ashtekar and Bojowald, which we cite. I might mention also that the literature on elimination of cosmological singularities in homogeneous models is now very large, for a recent review see Parampreet Singh , Are loop quantum cosmos never singular?, arXiv:0901.2750.

My view is that these papers together greatly strengthen the case for a conservative resolution. As we argue, IF the singularities are eliminated, THEN unitarity is likely a consequence. One then has just to use that unitary evolution to see what the dynamics predicts about the final state. It may in fact be the case that all the information gets to infinity, to find out one has to solve the unitary evolution. Discussion about ways to resolve the paradox without singularity removal are then very possibly non-sequitors, because if the singularity is eliminated the problem is solved.

Thanks Lee, it is probably most efficient to continue the private discussion. Just wanted to mention here for the sake of clarity that what we refer to as the information puzzle is a little different. For me this is the question of whether or not all the initial information is accessible to an observer staying outside the horizon at all times. I take it that you are asking whether the information is preserved "somewhere", which is a very different question.

So for example, if there are baby universes carrying all the information, the answer to the first question is no, and to the second one is yes. So, for me this scenario translates to information loss, and for you it doesn't.

The Horowitz and Maldacena option is not radical in the sense defined in the paper. Their modification is constrained to the region where one can expect quantum graviational effects to be strong, that's conservative. I find the motivation for imprinting the information in a boundary condition at the singularity weak, but that's a different point. I could indeed come to like that option if it wouldn't seem so ad hoc to me. Best,

I assure you that you have asked the simple question that you don't remember to have asked, and it is very trivial for everyone to check this fact.

Search this web page for: "But to one of your issues, how can anything happen at the horizon even if the curvatures are arbitrarily low. This is also well understood. In any quantum mechanical system with large degeneracies (as is typical for highly excited states), the following holds..." That's what Moshe wrote.

And you asked: "Why do I have highly excited states if the curvature is arbitrarily low?"

Sabine: I don't know who or what you are arguing with, but I never said anything of the sort that the black hole interior is empty or whatever it is you are trying to say.

I was not trying to argue with you in any way. I was answering your question why the information could get out of the black hole. And I was answering it because I was hoping that you would have actually paid some attention to the answer to this important question rather than being disinterested in (or even annoyed by) all the key concepts behind the answer.

Again, the answer is that at the level of microstates, the causal diagram derived from an empty classical black hole is not applicable which means that one cannot prove that no information can escape. That's what I mean by saying that microstates don't respect the causal rules of a simple classical black hole solution.

Sabine: Ah. And exactly how is this compatible with your above, correct, observation that what has crossed the horizon stays inside, and moreover can't even stay close by the horizon? I'm asking for a local dynamical explanation for what happens to the information. As far as I know fuzzballs create significant distortions of locality at horizon scales.

It is perfectly compatible. States with one spaceship - and the rest of the BH interior being (almost) empty - are much closer to the completely averaged black hole mixed states than a generic fuzzball solution, and the classical geometry around the spaceship becomes almost exactly applicable. When we already know that vast regions of the interior are almost flat, it guarantees that we must have already taken the average over very (exponentially) many microstates.

On the other hand, the geometry of the BH interior is never exact for a subset of states (or even one pure microstate), and it is never exactly true that the information cannot get from the spaceship outside the black hole - small effects can do it.

It's a normal thing for this information to do whatever it wants to do: on the contrary, the ability to hold the information isolated inside is an "emergent phenomenon" obtained by averaging over sufficiently many eigenstates so that the effective geometry (almost) mimicks the classical black hole and all objects have to respect the causal rules of this classical black hole. Again, individual microstates don't look like this, and they don't respect this causal diagram.

Correct, it has been lost for the physical observer in the asymptotically flat region. The point is however that the evolution remains unitary if you take into acount the full endstate, which includes the disconnected part. I personally don't think that's such a particularly compelling scenario, but it's certainly a possibility.

The problem with this statement about the preservation of the information in other universes is not that it is not compelling. The problem is that it is physically meaningless. For whatever non-unitary evolution, one could always argue that the information is preserved in another Universe or in God's memory, or whatever. In all these metaphysical and religious scenarios, the information is lost from the viewpoint of physics. It may be preserved from the viewpoint of metaphysics but I was talking about physics which measures the information, by the definition of physics, in the experimentally accessible universe only.

Sabine (to orbifold): Your argument is a non-starter. A) I was explicitly not referring to curvature singularities, but more importantly B) I wasn't saying if you don't have a singularity, you don't have a problem.

Of course that you were. Open your paper on page 3. You write: "But we do note that there is recent work that does show that, in a particular model of quantum gravity, black hole singularities are removed in a way that leads to the restoration of unitary evolution. This result has been derived in a study of the CGHS [9] model by Ashtekar et al in [10]. They find results that confirm earlier arguments in [12]. Part of the motivation of this paper is to put their results in a broader context."

Maybe you should read your paper before you discuss on the blog.

Sabine: If you want to provide a counterexample, you'd have to find a case with singularity but without paradox, and not a case without singularity but with paradox.

This counterexample has been mentioned about five times on this page already, too. I am talking about Maldacena 2001, the eternal AdS black holes. Figure 1 shows that he is talking about a spacetime with spacelike singularities. By constructing a dual boundary description with two boundaries, he is able to explicitly show that the information is fully preserved. One can say that the singularities are "resolved" but the resolution is not a new geometry which draws something completely different than singularities at the beginning or the end. The resolution is the AdS/CFT boundary dual which actually allows one to calculate what's happening in the spacetime, including the arbitrary vicinity of the two singularities.

Indeed, everybody can check this comment section to find out what I said. I have no time and no interest to play silly games like this.

That's what I mean by saying that microstates don't respect the causal rules of a simple classical black hole solution.

Thanks, fine. Now what is your problem? You have a solution approach, according to our terminology it is "radical", you can decide for yourself whether you find that flattering or insulting.

On the other hand, the geometry of the BH interior is never exact for a subset of states (or even one pure microstate), and it is never exactly true that the information cannot get from the spaceship outside the black hole - small effects can do it.

Does the fuzzball have an event horizon at all?

I think it is pointless to argue about what the interesting aspect of the information loss problem is, clearly your interests are elsewhere than mine. It seems to me btw this is the same point as Moshe and Lee have been discussing, see above comments for clarification.

I wasn't saying if you don't have a singularity, you don't have a problem.

Of course that you were. Open your paper on page 3. You write: "But we do note that there is recent work that does show that, in a particular model of quantum gravity, black hole singularities are removed in a way that leads to the restoration of unitary evolution. This result has been derived in a study of the CGHS [9] model by Ashtekar et al in [10]. They find results that confirm earlier arguments in [12]. Part of the motivation of this paper is to put their results in a broader context."

Maybe you should read your paper before you discuss on the blog.

Maybe you should try to understand what I was saying before commenting on it? The paragraph you quotes says very clearly: There is a model XYZ in which the singularity is removed due to quantum gravitational effects and the resulting evolution is unitary. This is very different from saying whenever you get rid of the singularity, you have solved the problem.

This counterexample has been mentioned about five times on this page already, too. I am talking about Maldacena 2001, the eternal AdS black holes. Figure 1 shows that he is talking about a spacetime with spacelike singularities.

I'm not interested in eternal black holes, and even less interested in eternal black holes in AdS space. I am interested in describing nature. We have stated in the paper which black hole spacetimes we are considering. Best,

I can therefore only imagine how this must be for you and others who have this as their profession when picking up to read such a book.

Well, as you can imagine I usually skip the first some chapters. How many introductions to special relativity does one really need to read in once lifetime? I therefore very much appreciate it if the author makes sure the reader doesn't miss anything by skipping these parts and states in the preface (as one often finds), if you know A, B, C you can skip chapters 2,3,4 etc.

Yes, the measurement process in quantum mechanics itself is non-deterministic and non-unitary. The problem with the black hole evolution however occurs already before that. One can then discuss however how much non-unitarity is really worrisome to begin with. There are certainly people who have considered the option of just accepting non-unitarity. It is however argued (quite convincingly it seems to me) that this generically leads to non-neglibile violations of energy conservation. I have the impression however the issue isn't yet completely settled. Best,

I didn't ask why the object that is supposed to describe a fermion is stable or static, I was asking why it has a specific descrete mass spectrum that happens to coincide with the masses of fermions we have measured.

You need a non-vanishing trace of the energy momentum tensor because otherwise the object doesn't describe a massive fermion. Best,

In that case, I don't understand why you're playing these games in such a shortage of time. You asked a question to Moshe, he answered it, you asked it again, and I answered it again, using different words. Then you denied that you had ever asked the question. What's the point here? In science, we are used to asking questions because we are actually interested in the answers.

Sabine: Thanks, fine. Now what is your problem? You have a solution approach, according to our terminology it is "radical", you can decide for yourself whether you find that flattering or insulting.

I or we no longer have any major problem because the problem has been solved at the qualitative level, to say the least. The solution I sketched is not mine, it is the summary of one of the most important results of the theoretical physics community in the last 10 years.

Whether you use one adjective or another - a more sensible one or, in your case, a less sensible one - has clearly no impact on the status of the solution to the information loss paradox.

Sabine: Does the fuzzball have an event horizon at all?

No, fuzzballs don't have any event horizons. Do you hear this statement for the first time? Event horizons are approximate notions obtained by averaging over all (or a huge number) of microstates. A particular pure microstate has a vanishing entropy which translates into a vanishing area of event horizons.

Sabine: I think it is pointless to argue about what the interesting aspect of the information loss problem is, clearly your interests are elsewhere than mine.

I don't think that the basic discussion about similar important problems in physics is about interesting vs uninteresting questions. It is about correct vs incorrect answers.

Sabine: There is a model XYZ in which the singularity is removed due to quantum gravitational effects and the resulting evolution is unitary. This is very different from saying whenever you get rid of the singularity, you have solved the problem.

The problem is that there is no model in which the removal of singularity can solve the information loss problem because this problem has nothing whatsoever to do with singularity.

Now you're just trying to marginalize this whole point into "just one model" but you wrote very clearly that the motivation for writing your paper was exactly the result of this "model" that you wanted to put into broader perspective.

At any rate, these issues about stronger and weaker language are not too important because all your statements, both the weak and the strong ones, are completely incorrect.

Sabine: I'm not interested in eternal black holes, and even less interested in eternal black holes in AdS space. I am interested in describing nature. We have stated in the paper which black hole spacetimes we are considering.

You were seemingly interested in them a few minutes ago because you were asking orbifold bh for a counterexample to one of your statements. At any rate, your implicit idea that the qualitative character of the solution to the information loss problems is very different for Maldacena's eternal black holes and for other black holes in quantum gravity is completely wrong, too. I could have used non-eternal black holes, too, including Schwarzschild in ordinary AdS - with the disadvantage that the singularity is further from the boundary in that case.

But I guess that you're not interested in this statement about the universality and rigidity of these results, either, so I profoundly apologize for having bothered you with physics.

Sure, I think we all understand that you are saying string theory has solved the problem, thanks for the clarification.

No, fuzzballs don't have any event horizons. Do you hear this statement for the first time?

I just wanted to make sure we're on the same page, since you said earlier the only option you consider viable is option (1). Just that this option has an event horizon. Funny, isn't it? What it amounts to is that you need a distortion of that causal structure (call it 'microscopical' or whatever) that allows information to not be confined to that region. I understand you are saying fuzzballs provide such a scenario. I never questioned that.

I'm not interested in eternal black holes, and even less interested in eternal black holes in AdS space. I am interested in describing nature. We have stated in the paper which black hole spacetimes we are considering.

You were seemingly interested in them a few minutes ago because you were asking orbifold bh for a counterexample to one of your statements.

My apologies. I guess I should have noticed by now that you are either unwilling or indeed unable to fill in details of a sentence that I consider obvious. In this case I was obviously talking about a counterexample to the statement that is in the paper.

your implicit idea that the qualitative character of the solution to the information loss problems is very different for Maldacena's eternal black holes and for other black holes in quantum gravity is completely wrong, too. I could have used non-eternal black holes, too, including Schwarzschild in ordinary AdS [...] I profoundly apologize for having bothered you with physics.

If you are interested in physics, then why don't you point me to a string-theoretical study of the formation of a black hole from e.g a pressure free collapsing dust (preferably in a spacetime that actually describes our universe) and subsequent evaporation of that black hole which does indeed have a quantum singularity but no information loss and thus provides the counterexample you were just claiming exists?

Sabine: I just wanted to make sure we're on the same page, since you said earlier the only option you consider viable is option (1). Just that this option has an event horizon. Funny, isn't it?

No, it's not funny at all. The figure (1) is the correct macroscopic description of the fate of a Schwarzschild black hole spacetime. However, the macroscopic picture (1) itself doesn't contain all the tools to explain what happens with the information.

To do so, one must actually look at individual microstates, and pure generic microstates don't look like (1) and don't have any event horizon. As has been written about 10 times (by Moshe and others) already, (1) is the "thermodynamic" limit of averaging over (almost) all of these microstates.

I will happily write this answer for the 12th time, too, but one may be slowly approaching a reasonable limit.

Sabine: My apologies. I guess I should have noticed by now that you are either unwilling or indeed unable to fill in details of a sentence that I consider obvious. In this case I was obviously talking about a counterexample to the statement that is in the paper.

I have given you counterexamples to the particular assertion in your paper but you wrote you were not interested in them. And in fact, you still seem to be completely uninterested in any counterexamples or any other physical topics relevant for the quantum physics of black holes.

Sabine: If you are interested in physics, then why don't you point me to a string-theoretical study of the formation of a black hole from e.g a pressure free collapsing dust (preferably in a spacetime that actually describes our universe) and subsequent evaporation of that black hole which does indeed have a quantum singularity but no information loss and thus provides the counterexample you were just claiming exists?

Well, the reason is very simple. Because, as every physicist worth the name understands, whether a black hole is born from a collapsing cloud of dust or from adding worthless manuscripts into a near-critically heavy neutron stars has absolutely no impact on the qualitative physics of the black holes. The resulting black holes clearly have the same properties (by all the no-hair theorems, thermalization, etc.) and the same way to encode the information.

String theorists are not writing special papers about the information loss of black holes created out of dust because such papers would be intellectually deficient combinations of two problems that have clearly nothing to do with each other and no author with a difficulty to see this simple point could ever learn string theory and write papers about it.

But once again, everyone, including non-string theorists, is free to write papers about anything she finds fit or conservative. He or she doesn't have to be affected by any standards that are natural elsewhere.

I will happily write this answer for the 12th time, too, but one may be slowly approaching a reasonable limit.

You can save yourself a lot of time if you would not try to "answer" questions I didn't ask. I understand that the microstates you are considering are not bothered the classical causality and that this effect happens on horizon scales. This is a scenario that according to our classification is "radical". I don't know what there is more to say.

Your notion of what is "physical," "natural," or "interesting" clearly does not match with mine, but then I already knew that.

The information content of your comments has approached zero. I have made my points clear, you are fuzzing around, probably upset - as usual - that I am not advocating string theory. It's an entierely useless back and forth, I herewith consider this exchange finished.

Come on, Sabine. If I understand well, Moshe and Lobos were just explaining us why the 'radical' solution is in fact 'conservative' and nearly established.

I am just a chemical physicist but there seems to be nothing strange about objects of a high entropy that have some internal structure that stretches across the full volume that these objects occupy in space.

What is important in GTR is whether in realistic situations with ordinary matter, one will contradict equations of GTR in circumstances where it should apply. And they say 'No', they will hold after the averaging, much like if we calculate the index of refraction of a gas (which otherwise behaves as smoothly as the vacuum) by averaging over the effect of all the complicated and chaotic atoms in this gas.

I don't actually know whether they can prove or show that GTR emerges by averaging over their complicated microstates but I guess they have some reasons to say so.

Respectfully, I would disagree that there is anything 'radical' about an internal structure of bound states of a high entropy.

Indeed it has become clear to me that our notion of "conservative" is not shared by other people. I can't say this came very unexpectedly. I just honestly don't know what good it is to argue on the use of words.

there seems to be nothing strange about objects of a high entropy that have some internal structure that stretches across the full volume that these objects occupy in space.

No, of course not. Except that the 'stretching' to fill that volume isn't in agreement with the classical causal structure of these objects, and that doesn't explain how microscopically the information is transferred from the matter that collapsed to the outgoing radiation. Best,

“Indeed it has become clear to me that our notion of "conservative" is not shared by other people.”

Yes from my admittedly unqualified perspective the fuss seems to focus around the choice of words, so perhaps you should consider subtitling your paper to better express one choice of meaning assigned to “conservative” found in the Webster’s , which say its “marked by moderation or caution” ; as a subtitle this could read:

“Solutions for the Black Hole information problem narrowed to those less likely achieving throwing the baby out with the bath water.”

Then again perhaps that’s too long a subtitle and therein requires further consideration :-)

It is really interesting that here - as in several previous instances - when Lubos runs out of arguments we get some anonymous or pseudoanonymous comments that echo what he couldn't convince anybody of believing.

1. How come that neither your nor Lubos are able to tell anybody which statement of mine allegedly contradicted which statement?

2. This merely expresses your disliking of our choice of words. There is nothing to "get" here.

3. I indeed disagree with my co-author on the relevance of these results and he knows that.

It seems very clear to me the problem with your paper vis. Lubos. You have used the term 'Conservative' when in fact you tend more towards the blue side of things, aka 'Liberal'. As Lubos is without a doubt 'Conservative' it would appear he is upset you have tried to steal or otherwise co=opt his identity.

Just trying to lighten things up a bit! I'll take a gander at your paper tomorrow but suspect it above my paygrade.

Re: "It is really interesting that here - as in several previous instances - when Lubos runs out of arguments we get some anonymous or pseudoanonymous comments that echo what he couldn't convince anybody of believing."

Sabine, I've just read your next post (huge fan!) and you are not only a notorious pessimist but an equally notorious paranoid.

Peter Shor, the point is precisely that the black hole should be thought of as a generic highly excited state of a unitary chaotic system. Those states are very dense, almost degenerate. To distinguish one of those states from the others you have to measure S bits of information.

If the information on the initial pure state is all encoded in the Hawking radiation, you have to measure S bits of information encoded in that radiation to decide which state you started with.

You could for example measure one simple quantity (like the total energy) to S decimal places. By the uncertainty relation that will take a very long time. Or you can measure the time sequence, e.g the same quantity at S different times. Or anything else really, as long as you gain S bits of information.

The point is that for any of those measurements you will need more than semi-classical gravity has to offer. The fact that you cannot distinguish the black hole states from each other, or from a thermal state, using order one bits of information (measuring simple quantities, whose complexity does not scale with the entropy, to a fixed accuracy, which also does not scale with the entropy) should not be surprising.

Dear Spinfoam, the coarse-graining (summing over many microstates) leads to gravitational description, see e.g. a paper by Alday, de Boer et al.

I don't think that they're extremely universal and show everything we want to know but they're surely a "proof of a concept". It may sound remarkable that by summing over many/all chaotic microstates, one gets such a simple description. On the other hand, that's what has to happen in any thermodynamic limit - which simplifies things.

Sabine: if you disagree (as you just wrote) with Lee Smolin who says that Ashtekar et al. models to "solve the loss by removing singularity" are important, you shouldn't have agreed to become a co-author of a paper whose main purpose is to promote these results and put them into broader perspective, as the paper itself claims.

Your discussion with Anonymous whether she or he's me is, well, amusing, but I understand that you probably can't settle it by an experiment so you have to rely on your natural beliefs.

Otherwise, Lee Smolin's unfortunate choice of words ("conservative") was clearly deliberate and meant to introduce bias - to present a fringe, unlikely approach as a sensible and serious one (at least for those who can be fooled by adjectives).

I think that physicists should stick to evidence and allow others to think which solution is conservative, especially if they know that the justification for their adjectives will be inevitably misunderstood by the readers.

Sabine, I've just read your next post (huge fan!) and you are not only a notorious pessimist but an equally notorious paranoid.

I should add that this combo is actually not that uncommon!

Thanks, I am glad you like the new post for you will probably see it on the front page for the rest of the week, I am presently somewhat stressed out.

The comment you are referring to was actually a rare expression of optimisim. I was thinking there can't possibly be two different people in the world that unable to extract meaning from simply phrased conversations. Now see where that optimism got me.

I agree on everything that is stated in the paper. Having a co-author does luckily not require to agree with that person neither on the motivation for writing the paper nor on the opinion about every single reference cited.

1) As I believe I also said to somebody else above, you can try to live with non-unitary evolution if you really want. There are certainly people who have investigated this possibility. Generically, non-unitary evolution (from the initial to the final state) however goes along with violations of energy conservation. I think the issue of how large these violations have to be and whether that could be acceptable is not completely settled. However, that is a solution attempt we have not considered in the paper. The point is not that there couldn't be something funny going on in the quantum gravitational region, the point is that this fun wouldn't neatly stay there but affect the evolution from one asymptotically flat region to another.

2) I don't think I ever said something about the question 'where the black hole entropy is coming from', I am not even sure what that means. But yes, for all we currently know, there is no way we will be able to measure Hawking radiation any time soon (except possibly the LHC does indeed create micro black holes).

3) I think it is doable with some more effort at least to construct models that can fill in this spot without causing any disastrous problems, and I am confident these will increase our understanding about what is going on under such extreme conditions. I don't know of any way how this could be experimentally testable. That doesn't mean however nobody will ever be able to find a way.

Thanks for your reply, amidst all this heated exchange of opinions!... Regarding the Planck scale, it is possible that astrophysical data from gamma ray bursts and Dark Matter detectors will provide some clues in the long run. But this is far from being a sure thing. I also hope (like everyone else) that LHC will help us understand what is going on in the TeV sector and (maybe) give us further hints on what's happening above this scale!

In any event, congratulations to you and Lee for a well-written report!

Maybe someone in this thread could give me an argument why causally seperated baby universe creation is a possibility that isn't automatically excluded by observation.

I realize that from the point of view of an observer in the flat space, he/she will still have an information loss problem. He will rightly conclude that information is lost in his universe and that physics in his local patch is nonunitary and its only in the full picture with all the baby universes taken into account that unitarity is restored.

Now shouldn't this imply drastic violations of energy conservation? From the point of view of the global evolution of the universe each time you create a blackhole, it acts like an energy sink. Wouldn't this completely alter the basic models of large scale structure formation? In fact you could imagine that it would change the FRW solutions by adding time dependant fields. You could go from a k = 0 universe to a k = -1 universe almost instantly! =/

Well, for one how many black holes do you think have completely evaporated during the history of our universe? Though it is hard to say with certainty, my (very conservative) estimate would be none. One can speculate about primordial black holes if you really want to.

However, more important than that, I think you have a confusion about the scenario we were considering:

shouldn't this imply drastic violations of energy conservation? From the point of view of the global evolution of the universe each time you create a blackhole, it acts like an energy sink.

When you create the black hole, it can carry a lot of energy indeed. Then it evaporates. And evaporates. And evaporates. Maybe some hundred billion years or so, depending on its initial mass. In the case with the baby universe, it just keeps on evaporating until the mass as measured by an observer at infinity vanishes. Then the interior disconnects. There is no loss of energy in the parent universe.

Best,

B.

___

@ All Anonymouses: Would you please be so kind to either use a pseudonym (chose option Name/URL, you don't have to enter an URL) or at least enumerate yourselves? It would make my life much easier. Thanks.

Sabine: I agree on everything that is stated in the paper. Having a co-author does luckily not require to agree with that person neither on the motivation for writing the paper nor on the opinion about every single reference cited.

what you write here is internally inconsistent. If you disagree with the motivation to write the paper - to promote Ashtekar et al. results and put them into a broader perspective - then you cannot possibly agree with "everything that is stated in the paper" because this motivation is explicitly stated in the first paragraph of page 3 of your paper.

And by the way, the rest of the paper is about the very same thing - that the Ashtekar "conservative" nuking of the black hole diagram - is a great idea (almost as great and as conservative as storing information in baby universes and remnants).

So you must still make your mind whether you agree with your paper or whether you think that the Ashtekar model is not an important insight showing how the black holes behave. Or, maybe, you don't have to make up your mind because none probably expects a coherent viewpoint on black holes, anyway.

In the paper we write "we do note that there is recent work that does show that, in a particular model of quantum gravity, black hole singularities are removed in a way that leads to the restoration of unitary evolution" followed by the reference Lee mentioned above, and later "Part of the motivation of this paper is to put their results in a broader context." That broader context being not constraining to a particular model.

What is your problem with that? That we have cited a paper by somebody you don't like? Gosh, Lubos, don't you have better things to do than telling other people what they should cite, how and when and whether you like the words they are using or not?

Exactly what is allegedly "inconsistent" about anything I wrote? Ashtekar's paper is interesting and a contribution to the discussion that certainly deserves to be cited in the context of our paper. However, as far as I am concerned it is a 1+1 dimensional toy model that he likes - as he said in his talk at PI, check recording if you want - because one can use it to lead students in one lecture through a calculation explaining what black hole information loss is all about. Then they quantize that model and find the singularity is resolved and unitary evolution restored. That is great. Just that it isn't clear to me how much that tells about the evolution of real black holes, and that is what I am ultimately interested in. I would also like to know better when the information comes out. This is not in the present publication but is supposed to be in an upcoming one as I hear. So I guess we will have to wait for that paper in preparation.

I hope that clarifies it. I would appreciate if you would stop trying to construct "disagreements" or "inconsistencies" that are not there.

1) It is possible that information is restored by the complete evaporation of the black hole as it reaches Planckian size. However, assuming that the information has not already come out in the Hawking radiation, it is obvious that this Planckian black hole will have to decay extremely slowly, since it has to release a huge amount of information using only a little energy. This behavior seems rather surprising(!) Does Ashtekar's model give this? If not, there's no way his story can be self-consistent. If it does that might convert this skeptic.

2) Contrary to popular belief, creation of baby universes does not necessarily lead to loss of information. This was heavily discussed in relation to wormholes twenty or so years ago, and was applied to black hole evaporation by Polchinski and Strominger.

3) I don't think it's accurate to say that little attention has been given to the "conservative" scenario in which the singularity is resolved and hence unitarity is restored. One finds much discussion of this in the papers from the mid 90s by Page, Polchinksi, ... But either the info comes out before the BH reaches the Planck scale (which requires spooky nonlocal effects), or the Planckian hole must have an extremely long lifetime, as noted in (1). What's missing is a direct and concrete calculation showing either of these possibilities.

Hi Bee:It seems that this discussion presupposes that a BH is formed. Is it possible that there are actually no BHs per this paper axiv07121130 "Fate of gravitational collapse in semiclassical gravity"? I always felt that unless one can define exactly how matter behaves under the extreme conditions that might cause a BH, then a BH is pure spectulation. Data that supposely supports BH existence could also be explained by some exotic state of matter that we currently no nothing about. BHs are not defined by just be a high density but by the event horizon. No BH, no event horizon, no paradox.

1) you would have to specify what assumptions you're making about the information/energy ratio. There's a much more natural, robust, and well-established bound constraining these things, the holographic bound, that implies that these small region of space can't contain that much information. It follows, among other things, that remnants and baby universes are simply impossible, in agreement with microscopic analyses of spectrum in all specific descriptions of quantum gravity we know as of today.

2) the 20-year-old wormhole picture that you seem to refer to is due to Hawking; and Coleman. Hawking himself denounced it in Virtual Black Holes 1995, primarily because it destroys the nice BH thermodynamical relations. Hawking surely doesn't believe the picture today, and already the 1995 paper also dismisses the Polchinski-Strominger variation of the picture.

The Polchinski-Strominger variation is similar and almost certainly not believed to be plausible by any major player who's been writing these papers 15 years ago. The progress simply went elsewhere and the relevance of the papers for physics gradually evaporated.

Coleman's general idea remains something that physicists keep in mind but the newer progress has eliminated all of its relevance for the information loss paradox. Such a radical thing is simply not needed today because contradictions that were once thought to be inevitable were shown to be absent in the consistent theory that is known to exist.

3) You would need a full new consistent theory of quantum gravity that would qualitatively disagree with string theory to achieve your goal at your desired accuracy. It is just extremely unlikely to get.

Sabine: if there are three opinions about the Ashtekar's paper(s)

1) it should be ignored and one should continue to freely say, like I and you (somewhere), that the removal of singularities is not sufficient to solve the information loss paradox

2) is an OK contribution to a discussion and good enough to be cited and mentioned

3) is important enough to serve as a part of motivation of writing another paper by other authors who want to put the paper into broader context,

I apologize but each two options above are inconsistent with one another. Now you invented 2) to interpolate between 1) and 3) but for me, 2) itself is still inconsistent both with 1) and 3) while 1) and 3) remain as inconsistent as before.

If you don't see this inconsistency, it is not too surprising that you can find dozens or infinitely many consistent enough and "conservative" theories of quantum gravity, among other cool things.

Lubos: I honestly don't think it is your business to tell me which papers I am allowed to cite in the introductions of my papers. Since you asked so nicely, I have offerened my opinion about Ashtekar's paper above. You can take that as option 4) and check the box. If you read through what I wrote here and in the paper you will find that there is nothing "inconsistent" about it. Best,

I always felt that unless one can define exactly how matter behaves under the extreme conditions that might cause a BH, then a BH is pure spectulation.

You don't need any extreme conditions to form a black hole. The formation of a black horizon can take place at arbitrarily low average density. I think must have written this two dozen times on this blog, but I will repeat it once again because it is a very common misunderstanding: The formation of a black hole horizon can take place at arbitrarily low density, and thus arbitrarily low background curvature. The relevant question is whether a total mass M is inside a region smaller than its own Schwarzschild radius R_H ~ 2M. The density in that region goes with M/R_H^3 ~ 1/M^2 and thus drops with larger total mass. For a large mass, the density is very small, it is far from being extreme in any sense.

The formation of a trapped surface is thus a very generic expectation of GR. You need radical measures to avoid it, not to get it. That btw is the reason why I don't find fuzzballs particularly plausible. Best,

Regarding 1: Indeed, that is exactly the point I did not understand about Ashtekar's model. At least in his talk he said the information would come out early (before the Planck phase), and I am skeptic about that for the same reasons you mention. That however is not in his paper that is published. I think it is supposed to be in the upcoming paper, I hope that will clarify this.

You are right that a direct and concrete calculation is missing. I hope to see one within the next years :-)

Bee:Thanks for the reply. By BH forming conditions I am talking about mass densities that exceed those of a neutron star or a quark star. Something between a BH and a quark star does not seem to be theoritically eliminated. The question regarding BHs has always been: Do they exist in nature? Not if they form what are their properties.

If you are talking about black holes of about solar mass, you can fiddle around with the equation of state of nuclear matter if you like. But that is hardly going to avoid black holes in general.

Are you satisfied that BHs actually exist?

Am I satisfied? Not sure what you mean with this. The formation of a black hole horizon is a very generic consequence of initial conditions in GR that plausibly exist throughout our universe. I find the evidence we have convincing. There are certainly other explanations - there are always other explanations for everything, but I'd say if it walks like a black hole and quacks like a black hole, I would call it a black hole. Unless I have good reason to throw out this conservative answer. And I see presently no good reason.

What is considered the biggest problem with sending the information of a Planck mass black hole out to a baby universe that looks like ours? The entropy?

Bee, I think I'm generally much more of a paranoid pessimist than you are so I think that's just another name for objective realist... and if only you could find a topic where Lubos and Amos could be on opposite ends of a debate, that would be real entertainment!

At least in his talk he said the information would come out early (before the Planck phase),

Hmm... looking at his paper he draws a Penrose diagram that looks like the standard one until one gets near the singularity, and he says that fluctuations in the geometry are small outside that region. It will be a neat trick if he manages to get the information out before the Planckian phase under those conditions.

I find it a bit worrisome that he doesn't in his paper discuss this issue of how the info gets out, except in a very superficial way. Perhaps it would have been advisable to forgo the "mission accomplished" title before getting this straightened out.

The reason might simply be that the paper is a PRL and they have a strict page limit. But yes, I too will be courious to see how they manage to do that, and I am looking forward to a more detailed explanation. Best,

Peter: look at my comment above. I think we have a case of non-standard use of scientific terms. The question the authors of this paper discuss, and Ashtekar as well, is whether information is "destroyed" by the singularity, or whether it passes through it. This may be an interesting question, or it may be a pseudo-question, depending how the singularity is treated in QG.

Be that as it may, this is not the question you and I (and nearly everyone ever thinking about the information paradox) have in mind, namely: does the information become accessible to an outside observer (i.e. observers like us), and if so when and how?

In Ashtekar's model the mission he accomplishes is a smooth passage through a singularity, he does not discuss whether the information can then end up at the original external region, and one may be skeptical for all the well-known reasons.

as a Gentleman, I will surely not annoy you with more inconsistencies! It's enough that I am annoyed by them.

Now I understand a bit better why you dislike the fuzzball or nontrivial BH microstates in general. You think that by avoiding the horizon, one is "radically" modifying GR, in the same way as Chapline who says that BHs don't exist and superconductors etc. stop them from forming. ;-)

Well, except that she's not modifying GR or denying their birth. In string theory, one can show e.g. that a graviton is exactly a vibration mode of a string, an object that seems to have much more internal structure. In fact, with high enough UV resolution, such a string extends over huge distances. But it's all just an unobservable illusion because this stringy graviton acts on matter exactly in the same way as a normal graviton - even though it also looks "extended".

In the same way, black holes may be demonstrated to have an entropy, so they must have microstates, and it just happens that the microstates look very chaotic.

But the issue one should try to understand is that the apparent "complexity" of such fuzzballs is only there if one studies really pure states and if one studies them with a perfect, Planckian resolution. Any averaging over space or many microstates will tend to smoothen the space and create horizons (or almost horizons).

The universal message above is that "purely gravitational" things zimply have extended structure according to string theory - gravitons and black holes are structured objects whose influence on strings and branes (all other matter) can be demonstrated to be exactly equivalent to the purely gravitational objects (in the case of BH, after averaging over microstates). They can't really look structureless because even gravitons and space itself is made out of strings.

All this stuff may sound very subtle but that's all possible because string theory is really a unifying theory of gravity and all other objects. So even though the fuzzball looks like a "completely different object" made out of non-gravitational "matter", it is really the same thing as a black hole microstate, and can be shown to act in the same way, on everything that can exist in the theory.

In these cases, one shouldn't really even talk about "emergence" because e.g. the stringy graviton mode is *exactly* the same thing as a graviton. The point here is not to approximate anything. The formalism just works in such a way that it is a precise identity. One is literally proving that gravitons and holes have a microscopic structure and what it is.

One can see similar things in Matrix theory, AdS/CFT, and elsewhere. For example, when one constructs a thermal state - out of microstates that can be explicitly constructed - it can be seen that e.g. in the path integral formalism, physics will have contributions from (Euclidean) black holes as long as the theory allows dynamical gravity in the bulk, which string theory always does.

Indeed, it seems you have come much closer to understanding my disliking. I don't need to tell you that, but let me add for the interested reader who might not know, that the 'fuzz' inside the fuzzball fills up the region that would have been the interior of the horizon. In fact, the extension of these objects is not Planck sized or anything nearby, instead it is a number dependent on the initial (string) setting times the Planck scale that sets their extension. In this way, one gets violations of locality on distances scales of the horizon, which can be arbitrarily large, and at arbitrarily low background curvature. According to the terminology in our paper, this is "radical".

It is certainly an interesting scenario. However, to solve the information loss problem it implies that some collapsing matter would have to fuzz out into some stringy state at arbitrarily low densities, somewhere around the time when classically the horizon would have formed - though I don't actually know of any dynamical investigation of the scenario that would describe such a collapse, so I am not sure one can actually conclude that. I also think the scenario assumes unbroken supersymmetry and most of the investigation has focused on extremal black holes, though I think there is some recent work to generalize this. Please correct me if I'm wrong, I am certainly not an expert on this.

I think we have a case of non-standard use of scientific terms... this is not the question you and I (and nearly everyone ever thinking about the information paradox) have in mind

Well, it is not of much use to discuss what either of us perceives as "standard use of scientific terms", but let me clarify the reason for our use of the term information loss problem. As far as I am concerned, what is paradoxical about the original setting Hawking discussed is that it leads us to conclude there is a disagreement between classical General Relativity and quantum mechanics - a non-unitary evolution - that can not simply be blamed on our not understanding of quantum gravitational effects. Non-unitary evolution implies information loss, thus the name information loss problem.

However, there is nothing particularly paradoxical about an observer in region A not having information about region B. Generically, this will also lead to non-unitary information, but this is not in conflict with quantum mechanics, it thus doesn't bother me.

Now one could of course say it is not nice if the observer at A never learns what is in region B. This reminds me of a discussion on the issue I had a long time ago with my first supervisor. His final argument for disliking such a possibility was that God would not disconnect himself from a region of his spacetime.

Bee, you can discuss whichever issue you find more interesting, we do seem to disagree on what issue is the real puzzle, but there is no point in arguing about that. However, I am just observing that there is a lot of people talking past each other here, in part because what you call the information paradox is not the conventional use of the term, therefore not necessarily what some of the people commenting (e.g. Peter) have in mind.

Bee, Moshe, I will keep mind that we might each attach personal meanings to the phrase "information loss".

One thing I find surprising is the discussion in Bee's paper in the "lifetime of decaying remants" section. Some doubt is cast on the claim that Planckian black holes must have an extremely long lifetime in order to get all the info out, assuming it has not already come out. But if a Planck mass object decays in roughly a Planck time, then it seems clear to me that it decays into a Planckian width pulse of order 1 quanta, and hence carries negligible information. Where could the needed large number come from?

Assuming that information is returned to the external observer, there needs to be some large number appearing in an unexpected way. Either you need nonlocal effects on scales much larger than the Planck length, or you need to believe in the existence of PLanck mass objects with lifetimes arbitrarily larger than the PLanck time.

I think this is a misunderstanding. We certainly didn't say anywhere that the remnant decays in Planck-time or something of that sort. That section was merely supposed to summarize the discussion and to say that if you look into the calculations that were actually done to address the question how long that last phase would take, there isn't much, and that what we could find doesn't seem to apply to the case without horizon and large internal volume. I have no strong opinion about that either way, I just don't find the status of arguments very conclusive. Best,

I am very puzzled by something. The string theorists here seem to think that the whole problem is virtually solved; one even sees sentences like, " This is also well understood."

If that is the case, what remains to be done?

One school of thought seems to be that essentially *nothing* remains to be done; all that remains is to translate the solution into the gravitational language on that side of the duality. And some people even seem to think that this is mere icing on the cake; maybe a gravitational description isn't really *necessary*. I think that's extremely short sighted. What is *really* needed is a way to get us out of AdS and into the real world; unless somebody can perform a miracle and bring Strominger's "dS/CFT" back to life....

Dear Peter, don't believe what you say. For example, there doesn't seem to exist any material difference between my and Moshe's attitudes.

Moshe is an Israeli Canadian while I have never been to these countries, we never shared any real teachers, and so on. Still, we end up with the same conclusions.

The qualitative answers to the big questions about the paradox are known by today, and if we're dreaming about something, it's a more "local" intuition or description of what's going on, especially inside the hole. But we're not guaranteed that such an additional thing exists so it is not clear whether the search for it makes sense.

Dear Dr Who: I don't believe that dS/CFT was a step to the real world or a new necessary ingredient to understand dynamics of black holes in the real world. The de Sitter space is much tougher - its empty version carries a huge entropy itself - and the predictable quantities in it are always "vague", affected at least the thermal radiation from the cosmic horizon.

dS/CFT has never worked and I am tempted to think that after years of sensitivity about it, Andy would agree today. If you neglect cosmological differences - the tiny acceleration of expansion - and study the local physics, the mystery of black holes in AdS, flat, or dS space is clearly equivalent.

Sabine: one more thing about the "fictitious nonlocality". If you consider e.g. Matrix theory (BFSS model), a matrix quantum mechanics with a U(N) group equivalent to M-theory for large N, the graviton - the simplest and lightest state in the theory - is an extremely complicated wave function of X-coordinates and theta-coordinates filled into N x N Hermitean matrices. If you look at the typical "size" of this bound state of D-branes, it scales like N^{1/3} (and around special directions, N^{1/9}).

The relevant physics is for infinite N, so this bound state looks extremely extended, nonlocal (imagine N being 10^{900}). But various dualities guarantee that if you have these "macroscopic clouds" going through each other, their interactions are almost exactly zero. It's a priori surprising, but with the knowledge of dualities, it is known to be true, and is a part of our "improved intuition".

In a similar way, the string itself is an extended object - the typical average x(sigma)^2 over the string is infinite if you send the UV cutoff to infinity. Still, these objects act as locally as you expect from a point-like graviton. The black holes are analogous in this sense, so this "nonlocality" of the fuzzball is largely undetectable.

The issue here is that the parts of the graviton/hole that are very far are associated with extremely huge frequencies (very fast degrees of freedom), so they average out very quickly to zero in all measurements (similar argument like one for the classical limit of a Feynman path integral where the typical trajectory that contributes is extremely unsmooth, too).

So only at the central regions of the graviton or hole, they "really" influence things. In the case of the string (or matrix) graviton, it acts like point-like particle, in the case of the black hole, it acts like an empty black hole after one averages over a few microstates (which makes phases in whatever average out to zero).

So in some sense, imagining that the black hole remains "horizonful" is a similar "classical" mistake as imagining that Feynman's path integral is dominated by smooth trajectories. It's not and the typical quantum fluctuation is such that the whole space, at least inside, looks very different.

Even in flat space, one could say that the typical configuration of QG in the quantum state is complicated. But it is "ordered", in some way. On the other hand, with the presence of event horizons, the horizon region must be able to "scramble" the degrees of freedom quickly, so that the black hole (inside the horizon) cannot be imagined as a quantum fluctuation around a particular smooth classical state. The very fact that the black hole quickly scrambles/thermalizes information is equivalent to the degrees of freedom being permuted in brutal ways. Still, it doesn't contradict the smooth character of the "mixed state" of these microstates.

Thanks for the explanation, that is interesting. I have one more question though. I think we are still talking slightly past each other as I said we have only considered real black holes that dynamically form, whereas you have been describing the static case. Could you elaborate somewhat one how you envision that collapse process to happen in the scenario you describe? Especially I would be interested in what happens to the distribution of energy density. Best,

Lubos: it can't be as simple as that -- you can't recover the information solely by the assumption that black hole microstates are really extended fuzzy objects. I assume that an infalling observer will experience falling through the horizon in the same way as predicted by the standard black hole geometry (if this is not true then you can throw out standard results like thermal Hawking radiation). If so, then you have the usual quantum xerox problem: the information about the observer is inside the horizon, but the outside observer says that this information is coming out with the Hawking radiation. At this stage, a string theorist might invoke the "black hole complementarity principle" to argue that the information hasn't really been duplicated. The trouble is that there is no independent evidence for this principle beyond its use in solving the above paradox, so the argument becomes circular. The point is that even after making your reasonable sounding assumptions, you still need to make a much more radical assumption later on for the story to work.

If a generic microstate has quasi nonlocal behaviour (I realize it averages out classically) and indeed from its point of view no horizon is formed, then couldn't you simply run the argument utilized against lorentz violating theories by say analyzing its behaviour in a highly boosted frame? In fact, are boosts even a symmetry of the system at that stage?

Dear Bee, it may be that I won't answer what is really interesting for you, but for me, the actual collapse of a star/dust that creates a black hole is a boring messy classical process.

Classical general relativity with the correct low-energy effective theory inserted is an OK description to describe all macroscopic facts about this collapse. And the microscopic details are so chaotic that it makes no sense to study them - one can't formulate any exact questions that I could see.

Precise questions become possible when energy etc. can be measured accurately, and to do that, one needs a lot of time - by the uncertainty principle.

The black hole birth is qualitatively similar to the birth of any other thing that eventually stabilizes. I don't know what's the best example - for example the igniting of the nuclear reaction in a nuclear power plant.

Well, it has some profile, space distribution etc. that engineers should better know a bit. But it follows some low-energy equations and I don't see any contradiction or puzzle here.

Before the object is born (or reactor works), the deviation from the ultimate stationary state is large, but it collapses exponentially (by quasinormal ringing modes etc.) as the stationary state is being approached. So sorry if you view the collapse as a part of mysterious quantum gravity - I see no quantum gravity in it whatsoever.

Dear Peter, if you ignore the relevant evidence and only use circular arguments, statements can sound circular. It still doesn't prove that they're untrue. In fact, it doesn't mean that there is no better evidence that actually proves that the complementarity is right. And be sure that this evidence exists.

In all the holographic descriptions we have, the "boundary" or otherwise non-gravitational description is manifestly mapped to the degrees of freedom outside the black hole only, so complementarity is manifest. So is the extended, difficult, "nonlocal" nature of the microstates, so the only thing that is left is to show that by coarse-graning, one can actually derive the classical physics in the interior, too, and I claim that this is now established at least in some specific examples, too. Papers were cited above.

This simultaneous validity of all these qualitative insights above - nonlocal physics that nevertheless looks local whenever it should - may have sounded improbable according to the intuition of the 1970s. But the experience teaches us otherwise and we must learn - and replace our common sense by an "uncommon sense" that actually incorporates what has been calculated.

an individual black hole microstate surely breaks the Lorentz symmetry spontaneously - much like any complicated state breaks all symmetries in the region it occupies.

On the other hand, this symmetry is restored if one considers expectation values averaged over all the microstates. So the "ensemble" of all these microstates preserves the Lorentz symmetry in regions near the horizon, at least with accuracy that becomes perfect for large black holes.

Such a restoration of the symmetry is a nontrivial assertion that is an interesting thing to check in any description of black holes we have - and it hasn't been checked in all of them, as far as I understand, even though from a path-integral perspective, it has to work.

But it is only possible because the fundamental laws of the theory still respect local Lorentz symmetry. It is pretty likely that if the symmetry is broken at the fundamental level, one will observe its violation even after any averaging over any microstates, especially if the physics near the horizon - which is extremely sensitive to the behavior of the theory - is considered.

In all the holographic descriptions we have, the "boundary" or otherwise non-gravitational description is manifestly mapped to the degrees of freedom outside the black hole only, so complementarity is manifest.

This of course contradicts your previous story. If CFT microstates are mapped to extended fuzzballs in the bulk, then for these states the CFT has access to the whole space. The event horizon might emerge after coarse graining, but this won't change the fact that the CFT is describing the entire space. Your version of complementarity is nothing more than the statement that physics outside the horizon is described by variables outside the horizon.

The basic problem is the following. In the fuzzball story, the information about an infalling observer comes out in the Hawking radiation in the same way that it would if the observer were falling into a ball of fire. In both cases, for the information to be imprinted in the radiation it is necessary that the observer be burned up in the process. So if you believe in the fuzzball scenario and in the usual rules of quantum mechanics, then you predict that the infalling observer will not fall smoothly through the would-be horizon, but will get destroyed. That's unavoidable. Maybe it's true, but it clearly signals a dramatic breakdown of semi-classical physics.

You can't just wave your hands and invoke complementarity here. These fuzzball geometries are horizon free and obey the usual rules of quantum mechanics as far as anyone knows, without some mysterious new complementary rules appearing.If AdS/CFT is a complete description then these new rules have to be derived from this starting point.

so the only thing that is left is to show that by coarse-graning, one can actually derive the classical physics in the interior, too, and I claim that this is now established at least in some specific examples, too. Papers were cited above.

Anyone following this line of research will know that nothing like this has been done in the context of a large semi-classical black hole.

Conversation has strayed quite a bit from the original one, which is probably a good thing. Let me just comment that there are some issues we know almost for certain to be correct - for example the observations of an outside observer in asymptotically AdS space are described by a unitary QM (we can write it down explicitly). I think you'd find very few people that are familiar with the evidence and think otherwise (call them mavericks if you will), including people who at some point strongly held an opposite viewpoint.

This is valuable because now we can make progress and ask different series of questions, like the ones Peter is asking here. For example what is the viewpoint of an infalling observer, and how does their semi-classical viewpoint emerge. Fuzzballs (horizon free geometries) are one proposal top deal with such issues, it is not without problems. I think it is fair to say the view of the community is split on these questions. That just means they are more interesting questions to discuss than yet another iteration of the same old arguments about the information paradox.

Lubos: to your question. First, we did share some teachers, I certainly think about Tom as one...but to the point, I like the viewpoint of generic non-locality, and approximate locality depending strongly on a specific limit and the set of questions asked.

Let me just say that the non-local quantities people discussed at various points in the past, like the size of the graviton in matrix theory, or the size of the string in perturbation theory, always strike me as formal non-measurable quantities. But again, I agree that the implied picture smells right.

It seems that once again we disagree on what is boring and what is interesting, which is a discussion that in itself I find boring. Let me therefore just add that as long as you can't describe the dynamical scenario - the collapse of an object into a black hole and its evaporation (or at least, as Peter suggests, something falling into a black hole and its information being reemitted) - you haven't even formulated the problem, not to mention solved it.

I assume that an infalling observer will experience falling through the horizon in the same way as predicted by the standard black hole geometry ... If so, then you have the usual quantum xerox problem: the information about the observer is inside the horizon...

The scenario Lubos is talking about doesn't have a horizon. It is actually the causal diagram in Fig 3 in our paper (even though he insists the only viable option is (1)). The difference is that he is envisioning information can come out before the Planckian phase because there are non-local effects on horizon scales. That is not the case we have considered in option 3 (in the "conservative" case information doesn't come out before the Planck phase), but that doesn't change the diagram. I don't want to put words into his mouth, but I think the underlying idea is somehow that the information falls into the fuzz, wanders around in there for some while but eventually finds its way out, which is possible because of the messed up causal structure. Best,

Just to reiterate, the following statements seem mutually incompatible:

1) A black hole is really a horizon free fuzzball geometry governed by the usual rules of quantum mechanics

2) An observer falling into a fuzzball experiences this roughly as they would falling into a standard black hole geometry

3) Information about the infalling observer is emitted to the outside by Hawking radiation well before the fuzzball/black hole gets to Planckian size.

Something has to give. As Bee remarks, it's not clear that there's even a proposal as to how the fuzzball scenario is supposed to work in detail.

I think that the main point of Bee's paper is correct: the only scenario that doesn't change the usual rules outside of the Planckian domain is one in which the information gets emitted in the last stages of Hawking radiation by a Planckian black hole whose singularity has been resolved. But of course this scenario requires these Planckian black holes to have an extremely long lifetime, and there is no evidence of this occurring.

Peter, the scenario in which the information is encoded in the Hawking radiation also does not require any modification of known physics. For a generic high energy state in any theory the deviations from thermality are very small, so you'd need some very fine measurements to distinguish the state of the Hawking radiation from a thermal one. Semi-classical gravity does not provide you with such fine probes, which is why the question of whether the Hawking radiation is exactly thermal or not is a question for quantum gravity.

Phrased differently: even in any ordinary QM system, say anharmonic oscillator, the question of whether perturbation theory is valid is quantity-dependent. So the fact that all curvature invariants are small outside the black hole only means that we can use semi-classical gravity for dealing with SOME calculations. WE get approximately the right answer as long as the quantities we calculate are not too complex, or we don't require too much accuracy.

Dear Moshe: Let's suppose the observer falls into the fuzzball and then the external observer carries out the needed fine measurements on the emitted Hawking radiation that encode all the information about the infalling observer. If, as you say, there is no modification of known physics, then since information can't be in two places at once, we conclude that the infalling observer has been burnt up (or bleached, as they say). But this contradicts the description that follows from using the standard black hole geometry. So one way or another, there has to be a violation of the usual physics.

Peter, as I emphasized above, all we know in high degree of certainty is that the Hawking radiation outside of the black hole encodes the information, and that this is not that surprising, and does not require any modifications of physics in places we thought it was valid. I agree that a more explicit solution, phrased in a more intuitive and local bulk language, is desirable.

The question of the infalling observer is a different one, personally I'm not committed to the fuzzball proposal, partially because of all the good issues you raise.

I also have to add that personally I am not that troubled by all the quantum xerox type paradoxes. The reason is that the statement that an observer (presumably modeled by some localized excitation) falls through the horizon is an approximate semi-classical one. In the exact quantum mechanics everything fluctuates and you cannot make this statement precisely. So, I am not sure one can build any sharp conflicts with QM using such an inherently semi-classical concept as the infalling observer. I may be wrong, but it seems to me you can explain away subtle differences by having small probability that the observer isn't precisely what you thought it was.

Note that this is very different for the external observer, sitting far away where the metric does not fluctutate much. That observer has every right to believe their observations are described by ordinary unitary time evolution.

Moshe, by "known physics" I was including the statement that an infalling observer just sees the usual smooth geometry, but if you remove this assumption then I agree there is no problem.

I have to say I'm surprised that this xeroxing doesn't bother you more. Either the infalling observer gets burned, or the fuzzballs have to be acting in a very different way than any other known complex excited system. For all known systems the burning is what makes it possible for the radiation to carry out the information.

Peter: I agree that an infalling observer should see a smooth geometry, which is why I am not comfortable with the fuzzball proposal. In my mind one can still can derive such an effective description (for an appropriate set of measurement described by low energy gravity), while having a complete description that is very different.

In such situations, not that uncommon in physics, you replace questions such as "what really happened" with more precise ones involving measurable quantities. The mental picture you employ depends on the set of questions you ask.

Anyhow, none of this is not in any conflict with the observation that the Hawking radiation outside the black hole encodes all the information, which is the only point I'm trying to make.

the scenario in which the information is encoded in the Hawking radiation also does not require any modification of known physics. For a generic high energy state in any theory the deviations from thermality are very small, so you'd need some very fine measurements to distinguish the state of the Hawking radiation from a thermal one. Semi-classical gravity does not provide you with such fine probes, which is why the question of whether the Hawking radiation is exactly thermal or not is a question for quantum gravity.

While the question whether Hawking radiation *is* thermal or not might not be a question for quantum gravity, the question how you *get* information from the initial state into the not-quite thermal radiation is. See, I have no problem with the radiation not being thermal per se. I agree that this could necessitate very fine propes. What I don't see is how you dynamically transfer the information from the collapsing object (or infalling observer) into the radiation without any substantial deviations from the semi-classical approximation well outside the region where you would expect it.

In the exact quantum mechanics everything fluctuates and you cannot make this statement precisely.

Except that there is no reason why there should be substantial fluctuations at the horizon. Best,

Bee, the question of "how" the information becomes accessible is different from "whether" it does. Since we now know with near-certainty that it does (in my opinion), it is time to discuss different scenarios and proposals for the "how" question, without getting distracted with the "whether" question any more. Just my opinion.

As for the "how" question, let me try to phrase my personal faith. Comments are welcome, I'm not really a religious type. So, let me describe the formation of evaporation of BH from the two perspectives of the infalling and outside observer.

For an outside observer, the matter forming the black hole becomes hotter and hotter as it reaches the horizon. It starts probing short distance physics. For coarse grained probes this is described effectively by having a stretched horizon: hot membrane just slightly outside where the horizon would be. If you have a complete theory of the outside observer, just as we do in AdS/CFT, we know how to calculate the deviations from that picture, but to be sensitive to those we need to go beyond semi-classical gravity. This is more or less well-established in the asymptotically AdS context.

The infalling observer viewpoint is less established. Maybe the following is not too far fetched:

Let us describe the last stages of the "burning" process from the would-be-infalling observer viewpoint. The basic point is that the set of natural (low energy, gravitational) probes available to that infalling observer is different. They probe naturally a different coarse-graining of the same system. Presumably, their coarse-grained probes can be described approximately by an effective metric which is the one inside the horizon. That picture becomes less and less accurate as you get closer to the singularity of that effective metric.

I think the key to this mental exercise is stop looking at the metric as the whole truth, and accept that it is an effective description valid only for specific type of observations. It is then not inconceivable that two observers, making very different coarse grained measurements, describe their partial truth using different mental pictures.

Moshe, I don't mind if there are two different mental pictures, but I do mind that the information about the infalling observer is in two places at once (with that observer inside the fuzzball and in the radiation). This means that the fuzzball is not obeying the usual rules of quantum mechanics.

Peter, I did not mention fuzzballs, because I doubt the burning process as viewed by an outside observer can be described using an effective geometry only.

But, to your question: in the scenario I described there only one information, and it propagates by a unitary evolution in the full theory. However, there is no invariant meaning to "where" it is. Since the infalling and outside observer are capable of asking very different set of questions, they will answer that "where" question very differently. Which only means that is not a good question to ask in the full story.

Ok, so you have a complicated microstate that spontaneously breaks Lorentz symmetry.

But then this means there are goldstone modes and higher energy states that do respect this symmetry (eg individual strings I guess).

So we go from a fundamental lorentz invariant theory to a complicated emergent mess that breaks locality somehow (incidentally are there any associated fuzzball operators that are gauge invariant?), but then that averages away (kind of like how lorentz symmetry is restored on the lattice in the continuum) in some classical statistical limit.

So i'm still unclear how locality is violated in all this, given the fundamental description in terms of strings, and surely that has to give way slightly if we are to believe bh complementarity and holography. Also, why are we counting fuzzball degrees of freedom rather than the more fundamental stringy ones?

Looking for a science process that reveals some of the quandary about what is presented helps toward that end may be interesting thinking in relation QGP processes?

Penrose (2004, p.803):

“Under normal circumstances, moreover, one must regard the density matrix as some kind of approximation to the whole quantum truth. For there is no general principle providing an absolute bar to extracting detailed information from the environment. Maybe a future technology could provide means whereby quantum phase relations can be monitored in detail, under circumstances where present-day technology would simply ‘give up’. It would seem that the resort to a density-matrix description is a technology-dependent prescription! With better technology, the state-vector could be maintained for longer, and the resort to a density matrix put off until things get really hopelessly messy! It would seem to be a strange view of physical reality to regard it to be ‘really’ described by a density matrix (…)”

Having recognition of muon detection processes in Gran Sassois it evidenced enough then that such a process(microscopic blackholes) help to orientate our thinking in that experimental sense. Not to ignore IceCube either.

It's a matter of having a larger perspective(bulk descriptions are fine to me:)while discussing the formalities. Lubos was working toward that end. While Moshe is being realistic yet still far from pinpointing. A preference perhaps.

Dear Moshe, I didn't know Tom was literally or effectively teaching you! OK, that changes much about my comment, of course. But still, you're not Czech, are you? ;-)

Peter: if you expand the gauge theory perturbatively etc., you see black holes with horizons, and you don't see inside. If you don't do such an expansion and study the microstates on the boundary, you do see the microstates and there's no horizon. There's really no contradiction here.

The low-energy description with GR - or SUGRA - only emerges in the planar limit in 1/N expansions, for large N, and if you do it, the GR with horizons and complementarity emerges. If you don't do it, there is nothing special about the interior because you don't see it. You don't see any smooth bulk geometry, after all, but the unitarity is as obvious as in any nongravitational system.

Moshe: I completely agree that the large sizes of the BFSS bound states etc. are unmeasurable. That was really my point. But don't you think that in a similar way, the large size of a BH microstate (or fuzzball, but let me avoid the word below) is analogous, at least with worse than Planckian probes?

Bee: that's interesting that you find the "interesting vs. boring discussion" boring because you're the only one who is trying to open this discussion all the time. I am not interested in it. I am interested in the "correct vs incorrect" issues.

I may be wrong, but it seems to me you can explain away subtle differences by having small probability that the observer isn't precisely what you thought it was.

Moshe,

If, with probability near 1, the information comes out, then if you believe conventional quantum information theory and the semi-classical view of a black hole, with probability near 1 the in-falling observer must be destroyed near the horizon.

It's possible that the observer can be saved (until he approaches the singularity) at the same time as unitarity can be saved, by some black hole complementary principle, but nobody has figured out how this works, and you can't say its conventional physics.

Peter Shor: the scenario I gave in my previous comment is consistent with QM unitarity and with each observer's viewpoint of the part of spacetime accessible to them by using only low energy probes (note that this expression has different meaning for both observers).

Of course there are a lot of details to fill out, especially on how the viewpoint of the two observers are related. So, it is definitely far from being established. But, this seems to me the minimal scenario that is not inconsistent with the known facts about low energy gravitational physics and quantum information theory, all well-established parts of physics. Maybe I'm wrong.

The only thing you sacrifice is the ability to ask questions that are not necessarily well-defined in the full theory, like "where" things happen. If the geometry (or more precisely geometries) are just effective descriptions of the situation for certain probes, in a certain limit, the question of "where?" would always be answered with another question: "using which probes?".

Well, Moshe, that's all very impressive in a way, though I fear that you severely underestimate the difficulties of making precise the notion of "geometry" as an "effective description" [of what?]

Still, if I may drag you back to the main point of Sabine's original post: why do you prefer this to the solution proposed by Horowitz and Maldacena, which allows us to dispense with weird things happening near the horizon? I find the H+M paper almost as amazing and stimulating as Maldacena's "eternal black holes" paper. It certainly deserves far more attention than fuzzballs.

As far as I understand the Horowitz-Maldacena paper (and I'm trying to translate it into everyday terms), it says that we have a definite quantum state at "the end of time," that is, at the singularity inside a black hole, as well as "the beginning of time," that is, the Big Bang. Wouldn't this mean that somehow, time runs backwards near the singularity. Can this really be made to work consistently? Should this be detectable in the neighborhood of black holes?

Pope, I don't understand the M-H paper very well, maybe I'll invest some time trying to do that. It may well be the way things work for an in-falling observer. I am also not sure it necessarily contradict the complementarity picture.

As for the effective description, this may be not as difficult or alien as you think. Lots of progress is being made in realizing the ways geometry can emerge from ordinary QM systems in certain limits. AdS/CFT is probably the best understood example, the gauge theory is the fundamental description, it doesn't look like a gravitational theory on AdS, not at all. Nevertheless, there is an AdS hiding in there, with gravitons and strings and black holes and all those other good things. They are all only approximate concepts, valid in a certain limit, provided you don't ask questions that are too probing of the underlying structure.

Peter Shor: If, with probability near 1, the information comes out, then if you believe conventional quantum information theory and the semi-classical view of a black hole, with probability near 1 the in-falling observer must be destroyed near the horizon.

I am sorry, Mr Shor, but if all the information gets out and if the semiclassical picture holds at the same moment, then one can derive that you are a pink elephant. Or anything else. Simply because these two things are incompatible with each other.

If there is an exact horizon, the information gets lost exponentially and it can never come out again, because of simple constraints of causality, regardless of your fairy-tales about the events near/at the singularity. That Hawking has proven by this simplified proof is pretty much equivalent.

The singularity is irrelevant: the causal limitations come from the horizon. I wonder how many centuries it will take before well-known academicians around physics start to take notice.

As I continue to read Prof. John Moffat’s book while looking at all frenzied comment activity that your most recent paper has raised, I can’t help but wonder, what if Moffat’s right? I realize that modified gravity theories don’t get much attention by way of respect, as the dark matter/dark energy scenarios are what's most broadly accepted. Yet what if in the off chance he is right, then all of this discussion either way would have little significance.

With his theory, there is no dark matter and the rapid expansion is explained with a repulsive aspect to gravity, by way of the consequence and being in combination with a fifth force (additional level of freedom). What however is most important relating to this discussion is there are no singularities or event horizons and thus no way to violate the 2nd law or better have reason to be concerned that it is. With all the problems that dark matter dark energy brings, along with the additional concerns entropy (information) loss raised here, I’m further left to wonder why this idea hasn’t received greater attention.

Strangely enough it also seems somewhat consistent with Smolin’s idea, that the only thing being non emergent is time, for both matter and energy emerge with t=0 in Moffat’s proposal lending no significance other then to mark when both a negative and positive time universes began. However this would not be what we recognize as the begiinning of time in general, yet strictly time as it relates to these universes. In other words the time that proceeded and continues is what Smolin might call waiting time, as in fundamental time. So if conservative is to be looked at as the criteria, as to be considered being what’s relevant, perhaps then it should be also asked if it this idea is not the most qualified?

The singularity is irrelevant: the causal limitations come from the horizon. I wonder how many centuries it will take before well-known academicians around physics start to take notice.

You are correct that the causal limitations come from the horizon, nobody every debated that. But that isn't the problem. You have yourself discussed a scenario without future horizon (see definition in paper) and without a singularity. Now the only thing you need to realize is that if the solution was quantum singular (see definition in the paper), the information would not only be caught inside either an apparent horizon (option 3) or indeed an event horizon (option 4), but it would actually be destroyed and lost in the singularity. The reason this doesn't happen in the fuzzball is that it it's quantum non-singular. If you think about it for a while you will realize that the scenario you are advocating is quite similar to our option 3, except that you are convinced information can come out before the Planckian endphase.

Lubos: Let me try again. Yes, it is true that semi-classical gravity can be thought of as a 1/N expansion. This means that if you compute something in this expansion, finding that higher order terms are more and more suppressed, you should conclude that any errors to semi-classical gravity are of order something like exp(-1/N). Now apply this to the infalling observere for very large N. In this expansion you will find that with roughly probability 1 the observer falls smoothly through the horizon, keeping his information intact. You therefore conclude with near certainty that this information can't be simultaneously measured in the Hawking radiation, if you believe in standard quantum mechanics. What you are demanding is that this semi-classical expansion break down at leading order even though direct computation shows it to be well-behaved. This is a logical possibility, but it's a dramatic breakdown of an expansion in a regime where general principles say it should be valid, and I don't know any analog of such a thing elsewhere in physics, so more "details" are needed, to put it mildly.

regarding your above comment with the infalling and outside observer, you write "we know how to calculate the deviations from that picture, but to be sensitive to those we need to go beyond semi-classical gravity." Could you be more explicit on what you mean with "go beyond semi-clasical gravity"? Best,

Peter Shor: I already answered that question. When you are careful to use only well-defined questions, you can see that the two perspectives on what happens to the infalling observer can be simultaneously correct, just as two descriptions of the same process, without any dramatic failure of perturbation theory in regimes where it is supposed to be valid.

I also think this is the only way you can keep what we know to be correct in GR, in the appropriate regime of validity, and keep QM unitarity intact. I think the main barrier to come to terms with this picture is attributing the spacetime metric more reality than it deserved, therefore assuming that questions like "where" various things happen have absolute observer-independent answers.

The main point is that the geometrical perspective summarizes the observations using low energy probes (which don't have too much resolution). Since those probes are different for the two observers, related by (classically) infinite boost, they will describe the process using effective metrics which are different from each other.

I may be wrong in all that, but I appreciate if you tell me how. Where precisely in the picture I drew above do I get a failure of PT in regimes it is supposed to be valid?

Dear Bee, I don't see how anything I advocate can possibly be summarized by option 3).

3) is described by a particular causal diagram, a causal diagram only makes sense when there is a nearly smooth geometry, and in any description where there is a smooth geometry in the framework I advocate, the spacetime looks so that the causal diagram is drawn as 1).

Whether one says that the information is killed, undergoes euthanasia, or reincarnates into another Universe near (or at) the singularity is a matter of untestable philosophy (or religion). What is important for physics is whether the information can get out where we decide whether the information was lost: to scri plus.

And it is the causal rules plus the existence of the horizon that imply, in the semiclassical picture, that the information can't get there. The philosophy around the singularity has nothing to do with these physical questions. It's interesting that you're among the people who like to say that proper high-energy physics - string theory - has become a philosophy, but when it comes to a particular example, you advocate religious questions instead of a proper rational analysis of measurable issues.

Dear Peter, the non-perturbative contributions to 1/N perturbative expansions don't go like exp(-1/N) but rather exp(-CN) or exp(-CN^2). Think twice.

Otherwise, sure, the "probability that one can extract the information" is not behaving continuously in the limit. It is "0" in the 1/N expansion but "1" in the accurate treatment. There is nothing inconsistent about it. It's an order-of-limits issue.

The resolution needed to get the information out becomes extremely fine as N goes to infinity and the black hole is kept large. If you ask whether you can get the information out with a fixed resolution, in Planck units, the probability would be a continuous function of N. You can't "practically" get it out from large black holes, neither for finite N nor for infinite N.

The discontinuities of the type you are bothered by are completely common in physics. For example, the microscopic description of N atoms is time-reversal symmetric for any N, but the thermodynamic, large N limit - a phenomenological theory of matter - is time-irreversible and contains terms like the friction (that is calculable from the microscopic laws, at least in principle). It is completely analogous to the black hole case. The analogy is "large N" = "large N"; "preserved information" = "time-reversal symmetry".

Let me elaborate upon the analogy a little bit because this debate looks nearly isomorphic to some debates with Sean Carroll who was saying similar bizarre things in the case of thermodynamics.

For finite N, the number of atoms, we have a time-reversal symmetric theory. It preserves the information, too. It is reversible. I think that in this case, it's the side that Sean Carroll is getting and it is analogous to the description in terms of black hole microstates or fuzzballs.

However, there exists an extremely important large N limit of the theory describing N iron atoms. It is the macroscopic theory of pieces of iron described by partial differential equations for an iron continuum. This theory knows about the density of iron, various types of torsion, stresses, and friction.

Many of the terms in these equations violate the time reversibility, having first time-derivatives in them. Also, the things is slowing down by friction. These are completely analogous processes to those in GR where black hole emits waves and, following the ringing mode patterns, approaches the static (e.g. perfectly spherical) shape.

Now, for finite N, the information is preserved and the evolution is reversible. But the strict infinit N limit is a "new emergent theory" that knows nothing about the individual atoms or pieces of fuzzballs. And this theory is not time-reversible, and kills information (classically, it shrinks the volume of phase space during the frictionful evolution, even in the iron case).

Now, Sean Carroll doesn't understand how physics can possibly predict that the entropy increases and doesn't decrease instead, even though the laws should be T-symmetric. That's his problem because it's important that the entropy does increase and not decrease and every theory that would say otherwise is ruled out by basic observations.

Of course, we also know theoretically why the entropy increases. Any coarse-graining increases the volume of the envelope of some states in the phase space. The initial states are "well-defined" regions of the phase space, because we always study well-defined initial conditions, while the future state is always determined from the initial one by the evolution laws, so it is "chaotic" and has higher entropy.

It's interesting to notice how this influencs the jump from the micro to the macro description. Carroll doesn't see how the friction could ever be derived from a microscopic theory. But it can be derived in a very transparent way, following variations of Boltzmann's H-theorem.

How does one see that the final state is "chaotic"? Well, one may assume "molecular chaos" - random velocities in the initial state. This is completely analogous to the averaging over the black hole microstates. When one does so, he ends up with time irreversible effective equations - either GR with horizons and information loss; or with a theory of matter continuum with friction and viscosity and dissipation.

Molecular chaos may be controversial because there's no "preferred" random distribution at the beginning. But the details of the initial distribution really don't matter for the growth of the iron entropy, horizon area, horizon itself, or irreversibility: the only condition is that we must avoid infinitely unlikely and contrived choices of the initial state that would evolve into a low-entropy final state. It's not that hard to miss the special "adjusted" initial states.

So once we average over some initial microstates (of fuzzballs; or the velocities of iron atoms), we inevitably end up with the effective description, in the large N limit, that is irreversible, dissipates, generates entropy, and so on.

Dear Peter, the non-perturbative contributions to 1/N perturbative expansions don't go like exp(-1/N) but rather exp(-CN) or exp(-CN^2). Think twice.

Touche.

But the rest of your response is just wrong. Think about it. It's just like the decay of an unstable state in QM via tunneling. THis vanishes to all orders in hbar, but tunneling gives a contribution exp(-c/hbar). This is a very small effect, and so the perturbative result that the state is approximately stable is almost correct. In perturbation theory the proton is stable, and so that must be approximately true, and indeed decays due to nonperturbative effects give it a very long lifetime. IN your example, at large N the system will exhibit time irreversibilty to an excellent approximation (this is how our world looks after all). I'm stating the obvious: perturbation theory is very accurate when the expansion parameter is small, and corrections to perturbation theory are then exponentially small.

So if perturbative semi-classical gravity says with probability one that on observer falls through the horizon in a smooth way, then this must be very close to the truth.

The potential loopholes, which is what Moshe is getting at, are quite different than what you are claiming.

I don't see how anything I advocate can possibly be summarized by option 3).

Let me explain: Option 3) depicts an asymptotically semi-classical spacetime without a future event horizon and without a quantum singularity, for definitions see paper. Correct me if I am wrong, but I think this has been the case you have been talking about. As far as I know, fuzzballs neither have an event horizon, nor a singularity. The diagram you insist is the correct one however clearly does have both an event horizon and a singularity. Maybe you should make up your mind.

3) is described by a particular causal diagram, a causal diagram only makes sense when there is a nearly smooth geometry, and in any description where there is a smooth geometry in the framework I advocate, the spacetime looks so that the causal diagram is drawn as 1).

The geometric is smooth in the asymptotic limit. It might not be smooth in a region where quantum effects are non-negligible, there one shouldn't trust the diagram. That is the region shaded in grey. It might not even make sense to speak of locality in this region. That however doesn't change the fact that this region is embedded in the asymptotically classical space-time. It does not have a clear boundary (as effects don't suddenly turn on, but become gradually more important), but it certainly can be contained within a well defined classical region.

It's interesting that you're among the people who like to say that proper high-energy physics - string theory - has become a philosophy,

It is quite pathetic how you continue to invent things I never said.

In case that is what you are referring to, I have on an earlier occasion asked the readers of this blog whether Physics will turn into Philosophy. Not only are you replacing Physics with String Theory, you also seem to have problems figuring out what the difference is between a question and a statement. (Now that I think about it, this is also evident in this comment section. Did it ever occur to you I ask questions not because I'm just stupid, but because I want to make sure we are talking about the same thing before we run into a misunderstanding?)

you advocate religious questions instead of a proper rational analysis of measurable issues.

Peter: "In your example, at large N the system will exhibit time irreversibilty to an excellent approximation (this is how our world looks after all)."

In both examples (iron and black hole), irreversibility (and information loss) holds to an excellent approximation for large N. In other words, whenever one chooses a resolution of probes and accuracy that is less than perfect, information is getting lost and the evolution is irreversible. There is no qualitative difference between the two cases.

The black hole example is not just analogous to the thermodynamic discussion: it is really a special case of it. I don't believe that Moshe disagrees with it because that would mean that he misunderstands basic thermodynamics, much like you do, and I see absolutely no reason to consider this hypothesis.

Bee: I insist on every letter I wrote and you just help to confirm my point. Neither of your ideas about the black holes has anything whatsoever to do with the black holes in the real world, or any world that at least remotely resembles the real world, unlike black holes from Maldacena's papers that are always in the same universality class, to one extent or another.

Lubos: I will try one last time to help you before I give up. Everyone agrees that a priori it is possible that the black hole information can come out in the radiation via small correlations that vanish in the infinite N limit. That by itself is fine, but the paradox is how to reconcile this with statements about an infalling observer carrying in information. Order by order in the 1/N expansion you will find that the observer travels in nicely, retaining his information. For very large but finite N this should then be true to excellent approximation. But if you believe in the usual rules of quantum mechanics the information cannot simultaneously be in the emitted radiation.

The potential loophole here is that perhaps there is some subtle way in which this information really can be in "two places at once". That's called black hole complementarity, and is what Moshe is advocating.

I really can't make it any simpler than that without the use of hand puppets.

Peter, do you agree then that complementarity does not require you to modify known physics in regimes it should apply? I think that point is crucial to me, because like you I'd be suspicious of any proposal that suggests otherwise.

Moshe: we'll have to first agree on what we mean by "in regimes it should apply". One might want to say that semi-classical results should hold whenever the curvature is low and one is asking sufficiently low energy question. But then one concludes that the infalling observer carries in information, and then the no xerox principle says it can't also be in the emitted radiation. Here I just assume that any information in the emitted radiation is in principle accessible to an external observer making low energy measurements, albeit with fantastic precision.

Alternatively, one might argue that the above is too strong a requirement, since the observeability of the information duplication relies on some superobserver who can simultaneously see inside and outside the horizon. So maybe one should only trust physics in regimes that can be tested without reference to such a superobserver. I would personally say that this by itself constitutes a modification of known physics, but perhaps this is just semantics.

In the above I am of course just summarizing the debates that went on regarding black hole complementarity in the early 90s.

Great, I think we understand each other perfectly, we are down to semantics and personal belief.

For me, references to unobservable quantities always raise a red flag, especially if there is an explicit confusion already on the table. I don't think this is the only context in physics for which such quantities (like that super-observer) get you very confused.

So, my inclination is to regard that kind of mental discipline as nothing unconventional, just some good thinking habits, but that is just a matter of personal taste.

Good, then I'm basically happy too. The true version of quantum mechanics/gravity may be such that it allows for information duplication as long as no one can actually observe this happening. I would just like to see this statement derived rather than asserted, as it is a bit vague to use as an axiom. And I'd like to know what are the precise conditions under which this information duplication can occur.

Agreed, qualitative scenarios are nice but calculations speak louder. Now that we have a microscopic description of a situation containing quantum black holes, we can start putting meat on this particular scenario. I'd say this is getting more and more plausible, but we are still pretty far off from claiming it is an inevitable fact of life. In particular the viewpoint of the external observer is natural in ads/cft, but the infalling observer is more mysterious.

(one minor point about the semantics, when two observers use different words to describe their partial knowledge of a single quantum state, duplication may be a misleading word to use).

I'd like to thank "Peter" and Moshe for their extremely helpful exchange, which has made me realise that black hole complementarity is far from being as silly as the fuzzball stuff made me think.

Moshe: you say about Horowitz-Maldacena: "Pope, I don't understand the M-H paper very well, maybe I'll invest some time trying to do that. It may well be the way things work for an in-falling observer. I am also not sure it necessarily contradict the complementarity picture."

Yes, I see what you mean, and in fact H+M express a hope that something like this might come out of their work, though I don't understand exactly what they say about this [towards the end of the paper]. That would be wonderful if it could be done. I do hope that you will eventually have a posting about H+M on your blog...

Peter Shor: Yes, the question as to the direction of time inside the black hole is crucial in H+M, but they explicitly deny that this will happen in their scenario; they devote a section of the paper to this very question. I think I will not try to paraphrase them... you might find this helpful:

http://dabacon.org/pontiff/?p=1207

Lubos M: Your errors in this discussion apparently stem from your misunderstandings re the foundations of statistical mechanics. I suggest that you consult

Peter, unlike Moshe, I don't see any partially rational reason that could be behind your extremely slow pace of understanding these simple things.

Peter: "Order by order in the 1/N expansion you will find that the observer travels in nicely, retaining his information."

Well, order by order in the 1/N (or "a", the atomic radius) expansion of the mechanics of 1 meter of iron, you will see that friction is slowing down its motion nicely, retaining the information about the initial state in exponentially decreasing degrees of freedom such as the relative velocity of two pieces of iron.

Until the observer hits the singularity - or the friction stops the iron completely. There is absolutely no difference here. I deliberately constructed the examples to be isomorphic so only a mad person could oppose them. It is disappointing but not shocking that you oppose them anyway.

Peter: "For very large but finite N this should then be true to excellent approximation. But if you believe in the usual rules of quantum mechanics the information cannot simultaneously be in the emitted radiation."

This statement is equivalent to the statement that "quantum mechanics is incompatible with complementarity". Clearly, the statement is wrong. The degrees of freedom inside are explicitly functions of the degrees of freedom that one may imagine to be in the Hawking radiation only.

For the iron case, there's still a perfect analogy. Two pieces of iron are crawling on top of one another. The relative velocity of these two places is like the quantities seen by the infalling observer - something that only makes sense in the thermodynamic limit.

You could also say that it is a quantum xerox machine to say that these relative macroscopic velocities evolve deterministically, yet they are independently imprinted in the atomic description. And you would be equally wrong. There's no doubling of information here. The macroscopic velocities are simply some special functions of the atomic velocities. There is no double counting here.

The only reason why the Hawking radiation could be banned from carrying the information is causality, but causality is only emergent in the strict infinite N case, i.e. in the 1/N expansions, but there's no exact causality in the exact finite N treatment.

I am sorry that this discipline of science may be too difficult for girls who play with puppets, but maybe boys who play with trucks could already get it.

Complementarity is fully compatible with the picture of difficult microstates - they're parts of the same framework. To decode the fuzzball inside the black hole, one must exactly know how it's connected to the exterior world near the horizon, i.e. one must know fine microscopic details about the Hawking radiation.

For the rest of the nasty "Pope" crackpots here. I haven't made any error anywhere in this discussion, unlike the gadzillion of errors made (and still being made) by the likes of Peter.

Lubos: you seem to be very interested in iron. That's nice. But we're actually discussing a different topic here.

Moshe: It would be good if there were an actual concrete computation one could imagine doing to check the complementarity idea. In one way or another, you need to have two operators (one describing an observer and one measuring radiation) fail to commute even though they are spacelike separated by an arbitrarily large amount and live in a region of arbitrarily low curvature. Furthermore, the amount of non-commutingness has to be of order 1, even though it is zero order by order in the semi-classical expansion. Finally, this should only happen when one of the operators is inside an even horizon, or there is some other reason why no single observer can compare results of measurements made by these operators.

Statements like "spacelike separated" undoubtedly become a bit fuzzy at the non-perturbative level, but the hard part is imagining that they get fuzzy enough when the curvature is arbitrarily low.

I can at least imagine how one would try to check something like this in AdS/CFT. But with current understanding the situation is effectively reversed, as it's very hard in this context to derive the ordinary causal structure and ordinary notions of locality.

Otherwise, as far as I know there is no direct evidence of this prediction of complementarity. The arguments in favor of complementarity are that it seems to be necessary if you demand that the info comes out in the radiation, and also that it doesn't lead to any obvious contradictions with the usual account of what an actual observer would measure.

Peter, I agree with everything you write (also, thanks for nice discussion, it helped me clarify my thoughts). In particular the best evidence for complementarity is indeed the fact that it minimally incorporates all of known physics in regimes it applies (shall I call such approach conservative?).

Something more concrete would be desirable, but we'd need to understand spacetime locality first. I have a feeling we are not that far off, because this time around we have a concrete model to discuss those things. We can calculate things and gather evidence, instead of arguing which proposal is more reasonable.

(incidentally, I seem to have mixed my Peters once or twice above, sorry.)

One minor point, about the commutator of the two operators: in semi-classical gravity all the questions you can ask give you ridiculously low amount of information (order one). So, the operators we have to discuss don't have a good semi-classical limit, and therefore you cannot say their commutator is zero in that limit.

The fact that either observer is so incredibly oblivious to the real nature of what is going on in the system, makes the idea of complementarity more plausible, I think.

So, the operators we have to discuss don't have a good semi-classical limit, and therefore you cannot say their commutator is zero in that limit.

You lost me there. Assuming the outoging radiation does carry the information, this should be measurable by an external observer making low energy measurements (albeit very precisely). So there should be a semi-classical operator that describes this. Are you saying that you need to know quantum gravity in order to measure these subtle correlations (I would say that you need QG to compute what these correlations are, but not to measure them once they are there).

I still don't understand how locality is violated in the fuzzball description. Seeing as how we must violate it at least weakly in order to avoid Hawkings argument and retain the nice picture of holography.

Peter, in the semi-classical limit you are only able to gather order one number of bits. Trying to gather order S number of bits, any way you'd like it, you'd need more than the semi-classical treatment.

I was assuming you are going to probe the system with very complicated operators to gather the required information. Alternatively you can also try to measure simple operators, but incredibly accurately. For getting this level of accuracy you'd need the small corrections provided by the full quantum gravity theory.

Either way, if you probe the system using only semi-classical gravity, you get a very coarse grained picture. This is an important fact in this whole story.

Peter, in the semi-classical limit you are only able to gather order one number of bits. Trying to gather order S number of bits, any way you'd like it, you'd need more than the semi-classical treatment.

I don't see that. If you put a black hole in a box it will evaporate away into a gas of approximately thermal radiation whose entropy is of order the black hole entropy. Using semi-classical tools I can "easily" distinguish between essentially all the microstates of such a gas without needing to know about quantum gravity.

Peter: presumably you'd measure some quantity, then calculate this quantity in semi-classical gravity for different states and use your measurement to distinguish the states. I'm saying that with any finite accuracy of measurement, and using only the semi-classical approximation for calculating properties of states, you will not be able to gather the required information to completely distinguish two generic states.

For example, generically all states with the same quantum numbers are non-degenerate. So, accurate measurement of the energy at infinity ought to distinguish them. However, the energy spacing is of order e^(-S), so in the semi-classical limit any energy measurement with finite resolution will get contribution from huge number of states.

completing the thought: even if you relax the requirement of finite energy resolution, and contemplate measuring energy to incredible accuracy, you'd still have to calculate the energy of states to that incredible accuracy in order to distinguish them. You cannot do that without the complete theory of QG.

Moshe: I agree that measuring the precise energy is very hard. E.g. the level spacing for a 4D Schwarzschild BH goes as M e^{-M^2}, which is tiny. But also for gas in a box, while you could try to determine the microstate by carefully measuring the energy, this would be incredibly hard, but there are other far easier ways to do it.

I'm arguing that if you could actually perform the experiment of collapsing matter into a black hole and letting it evaporate into a diffuse gas of radiation, a semi-classical observer could (by repeating the experiment enough times) thereby measure the S-matrix for this process. The hard part would be computing this S-matrix from first principles, but I don't see the obstacle to measuring it.

Peter: I see the distinction you are making. I am talking about the calculation, not the actual measurement (though there could be interesting issues there as well, especially for the infalling observer that has finite lifetime).

The description either observer gives to the system, using semi-classical GR variables, is a highly coarse grained one, that was my point. If both observers were describing the system in a language that was sensitive to all its fine structure, something like complementarity would be much harder to swallow.

I wonder what's the problem with information and black holes?Information is related to entropy, and entropy certainly isn't constant of motion of system thermodynamically or quantum mechanically, only classic mechanically, in Newtonian mechanics, which is 'trivial' limit of quantum mechanics, clearly more realistic world. So why that 'paradox'?best, A.

dS/dt>=0 , and so time reversibility of individual particles doesn't mean anything for a system of particles (an isolated system, say). Can you explain how is possible that classically information is lost , or are you saying that actually above form of 2.nd law is wrong, and it should be dS/dt=0 ?

I think I have stated the problem as I see it multiple times in this tread and in the previous one on the information loss problem. It's that the evolution is not unitary, which clashes with our understanding of quantum mechanics. All that talk about entropy doesn't get you anywhere if you don't know for certain what the entropy of the object or its radiation is. Best,

And so classically entropy increases , precisely because you include measurement in you model, and "if you wait long enough" you will only lose information, not gain it "from the sun", cause of repetitive measurement. Same with black holes.A.

Haha, dear Stefan, it's funny you are trying to fish something to throw discussion on personal.

And avoiding SCIENCE issues-.

I believe I made my SCIENTIFIC point very clearly, and any decoy you are trying to pull is very, how should I say... unprofessional.

I rest my case.

very best,A.ps. although I find it very admirable your try to defend your spouse even when she is obviously wrong. But I believe it is more helpfull to set someone straight than to support wrong opinions of others when they are wrong.

Gosh, I turn my back on this blog for 1 hour to run into a pharmacy and you guys get in a fight over nothing.

First, A., I don't know which 'case' you think you have made, but it is none.

I'm talking CLASSICALLY, the only way ENTROPY is defined. I hope you know CLASSICALLY what entropy is, do you?

It might have escaped your attention but CLASSICALLY there is no information loss problem, case rested. Besides this, Googling would have been sufficient to find that entropy also can be defined in quantum mechanics. It has the property that it remains invariant under unitary transformations, meaning in particular pure states evolve into pure states. To reiterate what I said above, the problem is that the evolution of black holes is seemingly not unitary (without measurement), in conflict with quantum mechanics as we know and like it.

Besides this, I think you suffer from a confusion about the case with dS>0. It does not mean the time-reversed evolution of a state with increased entropy does not exist, it means this time-reversed evolution is extremely unlikely to happen. I think this should explain my example with the sun. Whether getting that information is in practice feasible is a different issue.

However, as I have also said several times above, you might not be bothered that after measurement evolution is indeed non-unitary, but you should be bothered if prior to measurement it is, because it has unwanted side effects, such as violation of energy conservation that can in principle be arbitrarily large. As I said, you can try to play around with accepting some form of non-unitarity that might keep these side-effects small, there are people who are taking this path.

As to Stefan's comment, his and my exasperation with comments like yours is that they are completely unconstructive and merely show you have neither tried to follow the line of thought in my writing, nor my previous explanations in earlier comments. It is thus merely a waste of our time. I hope you understand that. Rest assured, it's nothing personal.

Take an arbitrary initial quantum state with total mass M. Let it collapse to a black hole. Let it evaporate. If Hawking's calculation holds, the emitted radiation depends solely on the mass (angular momentum, charge) of the collapsed matter. If it evaporates that way completely, the endstate is always the same for all initial states with the same mass. Thus, starting from the endstate you can not reconstruct the initial state. Evolution is not reversible, meaning it can't be unitary. (This is written in various forms in this post, in the earlier post, and in the paper.) You can then allow for deviations from the semi-classical limit in the Planckian regime, it follows the usual argument, see paper. Best,

Sorry, comments crossed. In the case of throwing something into the sun, you can 'in principle' reconstruct the initial from the final state before reduction through measurment (in which case you have the usual problem that this process is non-deterministic). Best,

“So if Hawking calculation holds we have a problem, and if don't we don't have a problem.”

Sorry for interjecting yet there is another possibility, although considered by most remote, and that is to consider that neither black hole singularities or event horizons don’t exist to begin with. That is GR is not quite right.

Recently I finished reading John Moffat’s book “Reinventing Gravity”m where he submits that his latest Modified Gravity Theory (MOG) predicts this. In this theory massive stars and super massive bodies at the centre of galaxies would form a final compact state he calls grey stars, where light (EM) is so bent that it has a hard time escaping, although a lesser amount does.

Unfortunately he doesn’t say how much greater in diameter it would be above the Schwarzschild radius radius, yet I know that a photosphere in a non rotating black hole extends 1.5 time the distance. For rotating ones there are two. I suspect then the calculated minimum radius is somewhere between the two. So there is some possibility that while Hawking’s calculations are correct but the model he uses foe gravity could be simply wrong.

This is not to say that I understand Moffat’s theory to be true yet, he has given ways it can be tested and thus falsified which seems more difficult using the more normal considerations.

So if Hawking calculation holds we have a problem, and if don't we don't have a problem. Do you think this problem is big enough to vote against HAwking calculation?

That's not the point. The point is to understand exactly why and where it fails and to get the correct answer.

Bee: listen, HAwking equations are semiclassical, meaning they very much include MEASUREMENT in them. Meaning no problem there.

You can't have your argument for quantum unitarity be based on semiclassical calculation, got it?

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My point then is that every semiclassical model includes measurement in it, meaning irreversibility is expected and it would be strange if there were not time-ireversibility

What is classical is the background field, and it is so to excellent approximation, the more massive the black hole, the better. What one computes is the propagation of a quantum field in this background. Its propagation should be reversible unless you perform a measurement on it, which you don't have to. If this is too complicated, think of it in terms of a scattering matrix, which I find more intuitive. You have an almost flat space in the beginning with some quantum states. They approach each other (form a black hole and evaporate) and you have outgoing quantum states. What are the transition amplitudes? Is this evolution unitary?

Besides this, let me repeat that the non-unitarity you generically get if you accept what you advocate can have unwanted side effects such as violations of energy conservation. Be careful what you wish for.

You could easily clarify your confusion if you'd look up any of the literature on the subject.

Well, I didn't read the book, but let me say that as much as I like John it doesn't make sense to me. See (as I said several times in this post and in earlier posts) a black hole horizon can form at arbitrarily small background curvature. GR is an extremely well tested theory in the weak curvature regime. If you want to generally avoid black hole formation you need to have significant modifications of the theory in regimes that we have well tested. I don't know how John envisions a solution to this, but I am pretty sure you'll have to bend your mind around quite a bit for this. Sorry for being so 'conservative' ;-p

Maybe you could clarify your confusion if you think about what you read.

I don't advocate nonunitarity, what I'm saying is that Hawking calculations are practically classical, meaning unitarity or nonunitarity is not an issue, since that term belongs to quantum domain.

Background field is classical, meaning it includes measurement, meaning you cant say it is so "to an excellent approximation". It is or it isn't. Measurement disrupts everything, in a rather DISCONTINUOUS way.

And so it is not "to an excellent approximation", but to a catasrtophic approximation.

As I have said above, the point is not to draw a picture with crayons, but to come up with a calculation that shows exactly when and where Hawkings calculation goes wrong and what the correct result is. Your argument is fundamentally flawed, you could equally well say that no process in our labs is ever unitary, because hey, we treat the background as classical. Yet, treating the background as classical is indeed, as I said, an excellent approximation - as long as quantum fluctuations of the background are negligible. Best,

I understand what you are saying, but you don't understand my answer. I am very sympathetic to the idea that the graviational field carries degrees of freedom that are relevant to the propagation and survival of information, but stating that alone doesn't solve the problem. To show that it does, you'll need to know how the quantum degrees of freedom are encoded in the quantum background, and that all the information from the initial quantum field (including the matter field) is contained also in the final state. You need to do that without causing strong deviations from the theories that we know and like which work perfectly well if the background is to good approximation classical - which is the essential ingredient to Hawking's result. You can put some quantum hair on the horizon if you like, as far as I know these attempts didn't go very far. If you claim that quantum effects of gravity are non-negligible, and relevant for the outgoing radiation, let me ask you once again: how so. And if you have solved the problem, why don't you go and publish a paper about it instead of wasting my time with your crayon drawings? Best,